Halacha

הלכה א
תְּרוּמָה וּתְרוּמַת מַעֲשֵׂר נֶאֱכֶלֶת לְכֹהֲנִים בֵּין גְּדוֹלִים בֵּין קְטַנִּים בֵּין זְכָרִים בֵּין נְקֵבוֹת הֵם וְעַבְדֵיהֶם הַכְּנַעֲנִים וּבְהֶמְתָּן. שֶׁנֶּאֱמַר (ויקרא כב יא) "וְכֹהֵן כִּי יִקְנֶה נֶפֶשׁ קִנְיַן כַּסְפּוֹ" וְגוֹ'. עֶבֶד כֹּהֵן שֶׁבָּרַח וְאֵשֶׁת כֹּהֵן שֶׁמָּרְדָה הֲרֵי אֵלּוּ אוֹכְלִין:
כסף משנה
1.
The great terumah and terumat ma'aser may be eaten by priests, both adults and minors, both males and females and their Canaanite servants,1Because Canaanite servants do not have a separate personal identity, but instead are considered as part of their master's possessions. A Hebrew servant, by contrast, is forbidden to partake of terumah as explained in Halachah 5. and their livestock,2The Sifra states that this applies only to animal fodder. Produce that is fit for human consumption may not be given to an animal. as [Leviticus 22:11] states: "When a priest will purchase a man, he is a financial acquisition...."
When the servant of a priest flees3In which instance, his master is no longer obligated to provide him with his sustenance. or the wife of a priest rebels against him,4The term "rebels" has a very specific meaning when used in this context: to deny a husband marital intimacy. In such an instance, her husband has the right to divorce her and is not obligated to pay for her sustenance, as stated in Hilchot Ishut, ch. 14. Nevertheless, until he divorces her, she is entitled to partake of terumah. they may still partake of terumah.

הלכה ב
תְּרוּמָה שֶׁל תּוֹרָה אֵין אוֹכֵל אוֹתָהּ אֶלָּא כֹּהֵן מְיֻחָס. אֲבָל כֹּהֲנֵי חֲזָקָה אוֹכְלִין בִּתְרוּמָה שֶׁל דִּבְרֵיהֶן בִּלְבַד. וּתְרוּמָה טְהוֹרָה בֵּין תְּרוּמָה גְּדוֹלָה בֵּין תְּרוּמַת מַעֲשֵׂר בֵּין שֶׁל תּוֹרָה בֵּין שֶׁל דִּבְרֵיהֶן אֵינָהּ נִתֶּנֶת אֶלָּא לְכֹהֵן תַּלְמִיד חָכָם. מִפְּנֵי שֶׁאָסוּר לֶאֱכל תְּרוּמָה טְמֵאָה. וְכָל עַמֵּי הָאָרֶץ בְּחֶזְקַת טֻמְאָה לְפִיכָךְ נוֹתְנִין תְּרוּמָה טְמֵאָה לְכָל כֹּהֵן שֶׁיִּרְצֶה:
כסף משנה
2.
Terumah required by Scriptural Law may only be eaten by a priest whose lineage [has been affirmed].5Hilchot Issurei Bi'ah 20:2 defines this term as follows: Anyone concerning whom two witnesses testify that he is a priest, the son of so-and-so the priest, and the descendant of so-and-so the priest, extending back until we reach a person whose lineage need not be checked, i.e., a priest who served at the altar. The restriction of the consumption of terumah to such priests is alluded to in the Book of Ezra 2:62-63): "These sought their genealogical records, but they could not be found, so they were disqualified from the priesthood. [Nechemiah] told them that they should not eat of the most holy offerings [which includes terumah] until there would arise a priest [who would inquire of] the Urim and Tumim [concerning their lineage]." Priests whose status is accepted on the basis of a prevailing assumption6I.e., they are regarded as priests by people at large even though there is no definite proof of their lineage. may partake only of terumah required by Rabbinic decree.
Terumah that is ritually pure, whether the great terumah or terumat ma'aser, whether required by Scriptural or Rabbinic Law is given only to a priest who is a Torah scholar7For only a Torah scholar can be expected to be versed in the knowledge and practice of the laws of ritual purity. The Sifri (to Numbers 18:28 cites a Biblical verse as support for this concept.
This is also alluded to by a Biblical narrative. II Chronicles, ch. 30, relates how King Chezekiah affected a renewal of Torah observance among the Jewish people. Among his efforts was to renew the observance of terumah and tithes, as it is written (30:4): "He told the people... to give the portions of the priests and the Levites so that they could strengthen themselves in the Torah of God." Chulin 130b interprets this to mean that these gifts should be given only to a priest or Levite who "is strong in his observance of the Torah of God." In the revision of his Commentary to the Mishnah (Challah 4:9), the Rambam writes that it is desirable and advisable to follow this restriction, but there is no prohibition against giving terumah to an unlearned priest.
because it is forbidden to partake of terumah that is ritually impure.8We are concerned that the impure priest will cause the terumah to become ritually impure and then partake of it while it is in that state. All of the unlearned people are presumed to be ritually impure.9The commentaries explain that we do not think that a common person will willingly transgress and eat terumah that is impure. Instead, the suspicion is that he will be impure and therefore make the terumah impure. Nevertheless, he will not realize what has transpired and will eat the terumah that he himself made impure. For these reasons, one may give impure terumah to any priest one chooses.10For it has to be burnt and any priest can perform that act. The Ra'avad differs with this ruling, maintaining that even such terumah should not be given to a priest who is unlearned. The Rambam's position can be supported based on the explanation given above that we do not suspect that the unlearned priest will deliberately transgress.

הלכה ג
יִשְׂרְאֵלִית שֶׁנִּשֵּׂאת לְכֹהֵן אֲפִלּוּ קְטַנָּה בַּת שָׁלֹשׁ שָׁנִים וְיוֹם אֶחָד תֹּאכַל בִּתְרוּמָה וְחָזֶה וְשׁוֹק. וְדִין תּוֹרָה שֶׁתֹּאכַל מִשֶּׁנִּתְאָרְסָה שֶׁהֲרֵי הִיא קִנְיָנוֹ. אֲבָל אָסְרוּ חֲכָמִים שֶׁתֹּאכַל עַד שֶׁתִּכָּנֵס לַחֻפָּה גְּזֵרָה שֶׁמָּא תַּאֲכִיל תְּרוּמָה לְאָבִיהָ וּלְאַחֶיהָ כְּשֶׁהִיא אֲרוּסָה בְּבֵית אָבִיהָ:
כסף משנה
3.
When an Israelite woman marries a priest, even a minor three years and one day old,11If a girl is younger than that, her consecration is not binding, as stated in Hilchot Ishut 3:11. she may partake of terumah and the breast and thigh [given the priests from the peace sacrifices].12Which may be eaten by all the members of a priest's household (Hilchot Ma'aseh HaKorbonot 10:5).
According to Scriptural Law, she may partake of these foods from the time that she was consecrated. Our Sages, however, forbade her from partaking of them until she enters the chupah.13According to Jewish law, marriage is a two-staged process involving kiddushin or erusin (consecration) and nissuin (living as man and wife). Today, it is customary to perform both stages at the same time. In the Talmudic era, by contrast, a significant amount of time - usually a year - was granted between the two. In this interim period, the woman was consecrated to her husband and relations between her and another man would be considered adulterous. Nevertheless, she lived in her parents' home and did not engage in intimacy with her husband. Nor was he obligated to support her. Our Sages feared that were a woman given terumah in this intermediate period, she might give it to her father or brother to eat. [This is a] decree, [instituted] lest she give her father and brother terumah to eat while she is a consecrated woman in her father's home.

הלכה ד
חֵרֶשֶׁת וְשׁוֹטָה שֶׁנִּשֵּׂאת לְכֹהֵן אֵינָהּ אוֹכֶלֶת בִּתְרוּמָה אֲפִלּוּ הִשִּׂיאָהּ אָבִיהָ גְּזֵרָה שֶׁמָּא יִשָּׂא חֵרֵשׁ כֹּהֵן חֵרֶשֶׁת וְיַאֲכִילֶנָּה. לְפִיכָךְ גָּזְרוּ שֶׁלֹּא תֹּאכַל חֵרֶשֶׁת בַּת יִשְׂרָאֵל כְּלָל:
כסף משנה
4.
A deaf-mute and a mentally or emotionally unstable woman who is married to a priest may not partake of terumah. [This restriction applies] even if her father concluded her marriage.14Both of these types of women are considered as incapable of marrying according to Scriptural Law. Since a deaf-mute's ability to communicate is so restricted, our Sages placed her in this category. Contemporary Rabbinic experts debate the status of a deaf-mute who was trained to communicate through other means.
Were such women to conclude marriages on their own, the marriage would not be binding (Hilchot Ishut 4:9). Nevertheless, the father of such a woman has the potential to conclude her marriage before she reaches the age of majority. If he does so, the marriage is binding according to Scriptural Law (ibid. 3:11). Even so, our Sages forbade such women from partaking of terumah for the reason stated by the Rambam.
[This is] decree, [instituted] lest a priest who is himself a deaf-mute marry a woman who is a deaf-mute and give her [terumah] to eat.15In contrast to a mentally sound priest, the marriage of a priest who is a deaf-mute is binding only according to Rabbinic decree. According to Scriptural Law, the marriage is of no consequence. Hence, such a priest's "wife" has no right to eat terumah For this reason, our Sages decreed that a deaf-mute who is the daughter of an Israelite16If, however, she is the daughter of a priest, she may partake of terumah by virtue of her father's privilege until she marries. should not partake of terumah at all.

הלכה ה
הַזָּר אָסוּר לֶאֱכל תְּרוּמוֹת שֶׁנֶּאֱמַר (ויקרא כב י) "וְכָל זָר לֹא יֹאכַל קֹדֶשׁ" אֲפִלּוּ הָיָה תּוֹשַׁב כֹּהֵן אוֹ שְׂכִירוֹ שֶׁנֶּאֱמַר (ויקרא כב י) "תּוֹשַׁב כֹּהֵן וְשָׂכִיר לֹא יֹאכַל קֹדֶשׁ". תּוֹשָׁב זֶה שְׂכִיר עוֹלָם. שָׂכִיר זֶה שְׂכִיר שָׁנִים. וְעֶבֶד עִבְרִי הֲרֵי הוּא כְּתוֹשָׁב וְשָׂכִיר. וְכֹהֶנֶת אֵשֶׁת הַזָּר הֲרֵי הִיא כְּזָר שֶׁנֶּאֱמַר וְכָל זָר בֵּין הוּא בֵּין אִשְׁתּוֹ:
כסף משנה
5.
A non-priest is forbidden to partake of terumah, as [Leviticus 22:10] states: "All non-priests17We have employed a literal translation, though somewhat clumsy in English, because of the exegesis of the verse later in the halachah. shall not partake of the consecrated food."18Sefer HaMitzvot (Negative Commandment 133) and Sefer HaChinuch (Mitzvah 280) include this as one of 613 mitzvot of the Torah. [This prohibition applies] even to a resident [worker] of the priest or his hired [worker], as [ibid.] states: "A resident [worker] of the priest or his hired [worker] shall not partake of the consecrated food."19Sefer HaMitzvot (Negative Commandment 134) and Sefer HaChinuch (Mitzvah 281) include this as one of 613 mitzvot of the Torah. [The term] "resident [worker]" refers to one hired forever. [The term] "hired [worker]" refers to one hired for years.20Even when a priest is obligated to provide for his worker's sustenance, since the worker possesses an independent financial capacity, he is not considered as the priest's "financial acquisition" (see Halachah 1) and may not partake of terumah. A Hebrew servant is comparable to a resident [worker] or a hired [worker].21Although a Hebrew servant is purchased by his master, he retains an independent financial capacity. Hence, even if he becomes nirtzah (see Hilchot Avadim, ch. 3), in which instance he must work for his master until the Jubilee year, he remains independent and may not partake of terumah.
We have followed the simple meaning of the Rambam's words which appear to interpret the verse as referring to an ordinary worker. The Kessef Mishneh notes that in Yevamot 70a and other sources, our Sages interpret the verse as referring specifically to a Hebrew servant. Why then, he asks, does the Rambam single out a Hebrew servant? He explains that the Rambam is implying that there is no difference in this regard between a servant sold by the court and one who sells himself into slavery.

A woman of priestly lineage who is married to a non-priest is considered as a non-priest, as [implied by the wording] "all non-priests" - i.e., neither he nor his wife.

הלכה ו
זָר שֶׁאָכַל תְּרוּמָה בְּזָדוֹן. בֵּין שֶׁהָיָה טָמֵא בֵּין שֶׁהָיָה טָהוֹר בֵּין שֶׁאָכַל תְּרוּמָה טְהוֹרָה בֵּין שֶׁאָכַל טְמֵאָה. חַיָּב מִיתָה בִּידֵי שָׁמַיִם שֶׁנֶּאֱמַר (ויקרא כב ט) "וּמֵתוּ בוֹ כִּי יְחַלְּלֻהוּ". וְלוֹקֶה עַל אֲכִילָתָהּ. וְאֵינוֹ מְשַׁלֵּם דְּמֵי מַה שֶּׁאָכַל שֶׁאֵינוֹ לוֹקֶה וּמְשַׁלֵּם. וְאִם אָכַל בִּשְׁגָגָה מוֹסִיף חֹמֶשׁ שֶׁנֶּאֱמַר (ויקרא כב יד) "וְאִישׁ כִּי יֹאכַל קֹדֶשׁ בִּשְׁגָגָה וְיָסַף חֲמִשִׁיתוֹ" וְגוֹ':
כסף משנה
6.
A non-priest who willfully partook of terumah - regardless of whether he was ritually pure or impure and regardless of whether [the terumah] was ritually pure or impure22The Radbaz notes that when a priest who is ritually impure partakes of terumah that is ritually impure, he is not liable for death. He asks: Why then is a non-priest liable for partaking of such terumah? He explains that for a priest who is holy by nature, impure terumah is considered defiled and he is not liable for partaking of it. For a non-priest, however, impure terumah is also considered holy and he is liable for partaking of it. - is liable for death at the hand of heaven, as [ibid.:9] states: "They shall die because of it, for they have defiled it." He is liable for lashes,23I.e., the court must administer lashes if witnesses observed the transgression and administered a warning. And if they do administer lashes, the sinner's transgression is expiated and he does not receive punishment by the hand of heaven. but does not make financial restitution for what he consumed, because [a transgressor] is never subjected to both lashes and a financial penalty.24This is a general principle applying in many different contexts. See Hilchot Na'arah Betulah 1:11; Hilchot Geneivah 4:9; Hilchot Sanhedrin 16:12. The Radbaz notes that generally, whenever there is a financial penalty and the obligation for lashes, the person is given the financial penalty and freed of lashes. In this instance, the opposite is true. He is given lashes and freed of the financial penalty. The Radbaz explains that in this instance, the person was originally liable for death at the hand of heaven. Hence, it is inappropriate that the transgression be absolved through a mere financial payment. If he partook [of terumah] inadvertently, [he must make restitution and] add a fifth, as [ibid.:14] states: "When a person eats sanctified food inadvertently, he should add a fifth."25One fifth of the new total; one fourth of the original amount.

הלכה ז
וּבַת כֹּהֵן כִּי תִהְיֶה לְאִישׁ זָר הִיא בִּתְרוּמַת הַקֳדָשִׁים לֹא תֹאכֵל. שְׁנֵי עִנְיָנִים נִכְלְלוּ בְּלָאו זֶה. שֶׁאִם תִּבָּעֵל לְאָסוּר לָהּ וְתֵעָשֶׂה זוֹנָה אוֹ חֲלָלָה כְּמוֹ שֶׁבֵּאַרְנוּ בְּהִלְכוֹת אִסּוּרֵי בִּיאָה הֲרֵי הִיא אֲסוּרָה לֶאֱכל בִּתְרוּמוֹת לְעוֹלָם כְּדִין כָּל חָלָל שֶׁהֶחָלָל כְּזָר לְכָל דָּבָר. וְאִם תִּנָּשֵׂא לְיִשְׂרָאֵל הֲרֵי הִיא אֲסוּרָה לֶאֱכל בַּמּוּרָם מִן הַקָּדָשִׁים שֶׁהוּא חָזֶה וְשׁוֹק לְעוֹלָם אַף עַל פִּי שֶׁגֵּרְשָׁהּ אוֹ מֵת:
כסף משנה
7.
[Leviticus 22:12] states: "When the daughter of a priest will marry a non-priest, she should not partake of the sanctified terumah." There are two concepts included in this prohibition:26This charge is considered as one of 613 mitzvot of the Torah by Sefer HaMitzvot (Negative Commandment 137) and Sefer HaChinuch (Mitzvah 283) .
a) that if a woman engages in sexual relations with a man prohibited to her and thus become a zonah27As explained in Hilchot Issurei Bi'ah 18:1, the halachic definition of the term zonah is: "A Jewish woman who engaged in relations with a man she was forbidden to marry, violating a prohibition that is universally applicable, or a woman who engaged in relations with a challal." or a chalalah,28The definition of the term chalalah is: "[A woman] born from [relations] forbidden to the priesthood. Similarly, any woman who is forbidden to the priesthood who engaged in relations with a priest becomes a challalah" (ibid. 19:1). as we explained in Hilchot Issurei Bi'ah, is forbidden to partake of the terumot forever,29The Radbaz emphasizes that although she is prohibited to partake of terumah, she is not liable for death at God's hands for willfully doing so. Nor is she required to pay an additional fifth if she does so inadvertently. as is the law with regard to any challal. For a challal is considered as a non-priest with regard to all matters;30None of the mitzvot and prohibitions associated with the priesthood apply to him. The Radbaz emphasizes that a challal is not entirely comparable to a non-priest, for a non-priest is liable for death at God's hand and a challal is not subject to such a punishment. and
b) that if she marries an Israelite, she is forbidden to partake of the portions of the sacrifices given the priests, the breast and the thigh forever,31I.e., in contrast to terumah as stated in the following halachah. even if she is divorced or widowed.

הלכה ח
אֲבָל הַתְּרוּמָה אוֹכֶלֶת אַחַר שֶׁגֵּרְשָׁהּ הַיִּשְׂרָאֵל אוֹ מֵת אִם לֹא הִנִּיחַ בֶּן מִמֶּנָּה. שֶׁנֶּאֱמַר (ויקרא כב יג) "וּבַת כֹּהֵן כִּי תִהְיֶה אַלְמָנָה וּגְרוּשָׁה וְזֶרַע אֵין לָהּ וְשָׁבָה אֶל בֵּית אָבִיהָ כִּנְעוּרֶיהָ מִלֶּחֶם אָבִיהָ תֹּאכֵל":
כסף משנה
8.
She may, however, partake of terumah after [her husband] the Israelite divorces her or dies provided he did not leave any children that she bore, as [ibid.:13] states: "When the daughter of a priest will become a widow or a divorcee and she has no descendants,32From that marriage. she shall return to her father's home as in her youth. She may partake of the bread of her father."

הלכה ט
מִפִּי הַשְּׁמוּעָה לָמְדוּ (ויקרא כב יג) "מִלֶּחֶם" וְלֹא כָּל לֶחֶם. חוֹזֶרֶת הִיא לִתְרוּמָה וְלֹא לְחָזֶה וְשׁוֹק:
כסף משנה
9.
According to the Oral Tradition,33See Yevamot 87a. [that verse was interpreted] "from the bread," but not all the bread. She returns to partake of terumah, but not the breast and the thigh.34Hence, if she willfully partakes of these foods even after being widowed or divorced, she is a transgressor and should be punished by lashes. See Hilchot Sanhedrin 19:4.

הלכה י
וְלֹא הַכֹּהֶנֶת בִּלְבַד אֶלָּא אֲפִלּוּ לְוִיָּה וְיִשְׂרְאֵלִית שֶׁנִּבְעֲלָה לְאָסוּר לָהּ הוֹאִיל וְנַעֲשֵׂית זוֹנָה אֲסוּרָה לֶאֱכל בִּתְרוּמָה לְעוֹלָם. וְאַף עַל פִּי שֶׁיֵּשׁ לָהּ זֶרַע מִכֹּהֵן:
כסף משנה
10.
[This concept applies] not only to the daughter of a priest, but to the daughter of a Levite or an Israelite. If she engage in relations with a man forbidden to her, since she became a zonah, she is forbidden to partake of terumah forever, even if she has a descendant born to her from a priest.35As the Rambam explains in Halachah 12, as long as an Israelite woman who was married to a priest has a descendant from the priestly seed, she is permitted to continue partaking of terumah even though she is divorced or widowed. This halachah explains that there is an exception to that rule. If such a woman becomes a zonah, she can no longer partake of terumah.
The Radbaz maintains that such a woman also is not liable for death at the hand of God if she partakes of terumah willfully, nor an additional fifth if she does so inadvertantly.

הלכה יא
לְפִיכָךְ הַשְּׁבוּיָה אֵינָהּ אוֹכֶלֶת בִּתְרוּמָה וְאַף עַל פִּי שֶׁאוֹמֶרֶת טְהוֹרָה אֲנִי. וְכָל שְׁבוּיָה שֶׁנֶּאֱמֶנֶת לוֹמַר טְהוֹרָה אֲנִי אוֹ שֶׁיֵּשׁ לָהּ עֵד כְּדֵי שֶׁתִּהְיֶה מֻתֶּרֶת לְבַעְלָהּ הֲרֵי זוֹ אוֹכֶלֶת בִּתְרוּמָה. וְהַנִּרְבַּעַת לִבְהֵמָה לֹא נִפְסְלָה מִן הַכְּהֻנָּה וְאוֹכֶלֶת:
כסף משנה
11.
For this reason, a woman who was taken captive36Whom we suspect engaged in relations, either willingly or unwillingly, with her captors and thus became a zonah. See the latter portion of Hilchot Issurei Bi'ah, ch. 18. may not partake of terumah even though she says that she was not defiled. Whenever the word of a captive woman who says that she was not defiled is accepted37See Hilchot Issurei Bi'ah 18:21 which explains that if a woman says "I was taken captive, but I was not defiled" before witnesses testify to her being taken captive, her word is accepted. or there is a witness38See ibid.:17 which states that in this instance, the testimony of one witness is acceptable. Moreover, the witness need not fit all the criteria that are usually required for witnesses in court. [who testifies to this effect] and she is permitted to her husband,39Even though he is a priest. she is permitted to partake of terumah. When a woman engaged in sexual relations with an animal, she is not disqualified from the priesthood40See ibid.:1. and may partake of terumah.

הלכה יב
יִשְׂרְאֵלִית שֶׁיֵּשׁ לָהּ זֶרַע מִכֹּהֵן אוֹכֶלֶת בִּשְׁבִיל בְּנָהּ בֵּין זָכָר בֵּין נְקֵבָה וַאֲפִלּוּ טֻמְטוּם וְאַנְדְּרוֹגִינוּס וַאֲפִלּוּ זֶרַע הַזֶּרַע עַד סוֹף כָּל הָעוֹלָם שֶׁנֶּאֱמַר (ויקרא כב יג) "וְזֶרַע אֵין לָהּ":
כסף משנה
12.
A daughter of an Israelite who has an offspring [she bore] from a priest may partake of terumah by virtue of her child. 41Provided she does not marry an Israelite as stated in Halachah 17. [This applies] whether the child is male or female or even a tumtum42A child whose genital area is covered by a mass of flesh and thus his gender cannot be determined. or an androgynus.43A person with both male and female sexual organs. Even the offspring of offspring until the end of time44I.e., her grandchildren or great-grandchildren who are descendants from a priest are alive even though her children themselves have died. [enable her to partake of terumah], as [indicated by the prooftext]: "She has no descendants."45I.e., the prooftext does not say, "She has no children" (Radbaz).

הלכה יג
כְּשֵׁם שֶׁזָּרַע יִשְׂרָאֵל מִכֹּהֶנֶת פּוֹסֵל אוֹתָהּ כָּךְ זֶרַע כֹּהֵן מִיִּשְׂרְאֵלִית מַאֲכִיל אוֹתָהּ וְאַף עַל פִּי שֶׁהוּא זֶרַע פָּסוּל. כֵּיצַד. בַּת יִשְׂרָאֵל שֶׁנִּשֵּׂאת לְכֹהֵן אוֹ כֹּהֶנֶת לְיִשְׂרָאֵל וְיָלְדָה מִמֶּנּוּ בַּת וּבָא עַל הַבַּת מִי שֶׁהוּא עֶרְוָה עָלֶיהָ אוֹ שֶׁנִּשֵּׂאת לְמַמְזֵר וּמֵתָה הַבַּת וַהֲרֵי הַמַּמְזֵר קַיָּם. הָיְתָה אֵם אִמּוֹ בַּת יִשְׂרָאֵל לְכֹהֵן תֹּאכַל בִּתְרוּמָה. בַּת כֹּהֵן לְיִשְׂרָאֵל לֹא תֹּאכַל:
כסף משנה
13.
Just as the descendants from an Israelite [born] to the daughter of a priest disqualify her [from partaking of terumah], so too, the descendants from a priest [born] to the daughter of an Israelite entitle her [to partake of terumah]. [This applies] even if the descendants are of blemished lineage.
What is implied? A daughter of an Israelite married a priest or the daughter of a priest married an Israelite and [that woman] gave birth to a daughter. A person who is an ervah46Marriage between the two would be either adulterous or incestuous. for the daughter entered into relations with her or [the daughter] married a mamzer47A person of blemished lineage coming from either an adulterous or incestuous relationship. [and the daughter gave birth to a baby which is a mamzer]. [Afterwards,] the daughter dies, but the mamzer remains alive.48Thus the offspring descendant that initially either enabled or disqualified a woman from partaking of terumah is no longer alive. Nevertheless, since there is a descendant of the relationship alive - even though the descendant is of blemished lineage - the woman's status remains the same as the Rambam concludes in the following halachah.

הלכה יד
הָא לָמַדְתָּ שֶׁהִיא אוֹכֶלֶת בִּשְׁבִיל זַרְעָהּ וְאַף עַל פִּי שֶׁאוֹתוֹ הַזֶּרַע פָּסוּל וַאֲפִלּוּ אֵינוֹ יִשְׂרָאֵל. וְאֵין צָרִיךְ לוֹמַר שֶׁאִם הָיְתָה לָהּ בַּת מִכֹּהֵן אַף עַל פִּי שֶׁהַבַּת נְשׂוּאָה לְיִשְׂרָאֵל וַאֲפִלּוּ נִתְחַלְּלָה הֲרֵי אִמָּהּ אוֹכֶלֶת בִּשְׁבִיל הַבַּת הַפְּסוּלָה:
כסף משנה
14.
If [the mamzer's] grandmother was the daughter of an Israelite who [married] a priest, she may partake of terumah. If she was the daughter of a priest who [married] an Israelite, she may not partake of terumah. Thus we learn that [the daughter of an Israelite] may partake of terumah by virtue of her descendants even though the lineage of that descendant is blemished, even though [the descendant] is not even [on the level of an ordinary] Israelite.49Our translation follows the version found in authentic manuscripts of the Mishneh Torah. The version found in the standard published text translates as "even if he is not Jewish" which is obviously incorrect as indicated by Halachah 16. See also Radbaz. Needless to say that if a woman [who married a priest] has a daughter born to her by him - even if the daughter is married to an Israelite and even if she became a challalah - she may partake of terumah by virtue of the daughter of blemished lineage.50Obviously, as long as her husband, the priest, is alive, she may partake of terumah regardless. The entire issue of the status of her descendants arises only when her husband has died.

הלכה טו
כַּיּוֹצֵא בּוֹ הַכֹּהֶנֶת שֶׁאֵינָהּ אוֹכֶלֶת מִפְּנֵי זַרְעָהּ שֶׁמִּיִּשְׂרָאֵל אַף עַל פִּי שֶׁאוֹתוֹ הַזֶּרַע כֹּהֲנִים. כֵּיצַד. בַּת כֹּהֵן שֶׁנִּשֵּׂאת לְיִשְׂרָאֵל וְיָלְדָה מִמֶּנּוּ בַּת וְהָלְכָה הַבַּת וְנִשֵּׂאת לְכֹהֵן וְיָלְדָה מִמֶּנּוּ בֵּן. הֲרֵי זֶה רָאוּי לִהְיוֹת כֹּהֵן גָּדוֹל מַאֲכִיל אֶת אִמּוֹ וּפוֹסֵל אֶת אֵם אִמּוֹ וְאַף עַל פִּי שֶׁמֵּתָה אִמּוֹ וְזֹאת אוֹמֶרֶת לֹא כְּבֶן בִּתִּי כֹּהֵן גָּדוֹל שֶׁהוּא פּוֹסְלַנִי מִן הַתְּרוּמָה:
כסף משנה
15.
Similarly, the daughter of a priest may not eat by virtue of her descendant from an Israelite husband, even if that descendant is a priest.51If, however, she remarries a priest she may partake of terumah, as stated in Halachah 18.
What is implied? A daughter of a priest married an Israelite and gave birth to a daughter that he conceived. That daughter married a priest and gave birth to a son that he conceived. [This son] is fitting to become a High Priest. He enables his mother52Who is the daughter of an Israelite. to partake of terumah and disqualifies his maternal grandmother [from doing so].53In this instance as well, obviously, as long as her husband, the Israelite, is alive, she is disqualified regardless. The entire issue of the status of her descendants arises only when her husband has died. [This applies] even if [the priest's] mother dies. [The grandmother] can say: "[One should] not be like my grandson, the High Priest, who disqualifies me from partaking of terumah."

הלכה טז
הָעֶבֶד אֵינוֹ פּוֹסֵל מִשּׁוּם זֶרַע וְאֵינוֹ מַאֲכִיל. כֵּיצַד. כֹּהֶנֶת שֶׁנִּשֵּׂאת לְיִשְׂרָאֵל אוֹ יִשְׂרְאֵלִית שֶׁנִּשֵּׂאת לְכֹהֵן וְיָלְדָה מִמֶּנּוּ בֵּן וְהָלַךְ הַבֵּן וְנִכְבַּשׁ עַל הַשִּׁפְחָה וְיָלְדָה מִמֶּנּוּ עֶבֶד וּמֵת הַבֵּן וַהֲרֵי הָעֶבֶד קַיָּם. הָיְתָה אֵם אָבִיו שֶׁל עֶבֶד זֶה בַּת יִשְׂרָאֵל לְכֹהֵן לֹא תֹּאכַל בִּתְרוּמָה. הָיְתָה בַּת כֹּהֵן לְיִשְׂרָאֵל תֹּאכַל שֶׁאֵין זֶה זֶרַע שֶׁהָעֲבָדִים אֵין לָהֶם יִחוּס:
כסף משנה
16.
The descendants of a servant do not disqualify [a woman from partaking of terumah], nor do they enable [a woman to do so].
What is implied? The daughter of a priest married an Israelite or the daughter of an Israelite married a priest. A son was born to that woman. The son [then] went and became attached to a Canaanite maid-servant and conceived [a son] with her. [That son is] a servant.54See Hilchot Issurei Bi'ah 12:13. [The following rules apply if the woman's son] dies and the servant remains alive: If the servant's paternal grandmother was the daughter of an Israelite who had married to a priest, she may not partake of terumah.55For it is as if she has no offspring from her marriage to the priest. If she was the daughter of a priest who had married an Israelite, she may partake [of terumah], because this offspring is not considered as a descendant, because the concept of parental lineage does not apply with regard to servants.56As stated in Hilchot Yibbum ViChalitzah 1:4 and Hilchot Avadim 9:3, among the implications of this concept is that we pay no attention to the parental lineage of a servant's father. Instead, it is as if he was conceived by his mother alone. There are other implications of this statement, as indicated by Hilchot Ishut 15:6, et al.

הלכה יז
בַּת יִשְׂרָאֵל שֶׁנִּשֵּׂאת לְכֹהֵן וּמֵת וְלָהּ מִמֶּנּוּ בֵּן וְחָזְרָה וְנִשֵּׂאת לְיִשְׂרָאֵל לֹא תֹּאכַל בִּתְרוּמָה. מֵת הַיִּשְׂרָאֵל וְלָהּ מִמֶּנּוּ בֵּן לֹא תֹּאכַל בִּתְרוּמָה מִפְּנֵי בְּנָהּ שֶׁמִּיִּשְׂרָאֵל. מֵת בְּנָהּ מִיִּשְׂרָאֵל אוֹכֶלֶת בִּשְׁבִיל בְּנָהּ הָרִאשׁוֹן:
כסף משנה
17.
[The above concepts are also relevant in the following instance.] The daughter of an Israelite married a priest and he died. She had borne a son to him. Afterwards, she married an Israelite. [Hence,] she may not partake of terumah. If her Israelite [husband] died, but she bore him a son, she may not partake of terumah because of that son. If that son dies, she may partake of terumah by virtue of her first son.57Who is a priest.

הלכה יח
בַּת כֹּהֵן שֶׁנִּשֵּׂאת לְיִשְׂרָאֵל וְיֵשׁ לָהּ מִמֶּנּוּ בֵּן וְחָזְרָה וְנִשֵּׂאת לְכֹהֵן תֹּאכַל בִּתְרוּמָה. מֵת וְלָהּ מִמֶּנּוּ בֵּן תֹּאכַל בִּתְרוּמָה. מֵת בְּנָהּ מִכֹּהֵן אֲסוּרָה לֶאֱכל מִפְּנֵי בְּנָהּ שֶׁמִּיִּשְׂרָאֵל. מֵת בְּנָהּ שֶׁמִּיִּשְׂרָאֵל חוֹזֶרֶת לְבֵית אָבִיהָ כִּנְעוּרֶיהָ וְאוֹכֶלֶת בִּתְרוּמָה לֹא בְּחָזֶה וְשׁוֹק:
כסף משנה
18.
[Similar concepts apply when] the daughter of a priest marries an Israelite. [If] she bore him a son and then married a priest, she may partake of terumah.58By virtue of her marriage to the priest. If [her second husband] dies, but she had borne him a son, she may partake of terumah.59By virtue of her son. If her son conceived by the priest dies, she is forbidden to partake of terumah because of her son conceived by [her first husband,] the Israelite. If her son conceived by the Israelite dies, she returns to her father's home as in her youth. She may partake of terumah, but not of the breast and thigh [of the peace offerings].60As stated in Halachot 7-9.

הלכה יט
בַּת יִשְׂרָאֵל שֶׁנִּשֵּׂאת לְיִשְׂרָאֵל תְּחִלָּה וְיֵשׁ לָהּ מִמֶּנּוּ בֵּן וְחָזְרָה וְנִשֵּׂאת לְכֹהֵן אוֹכֶלֶת בִּתְרוּמָה. מֵת וְלָהּ מִמֶּנּוּ בֵּן אוֹכֶלֶת מִפְּנֵי בְּנָהּ הָאַחֲרוֹן שֶׁהֲרֵי הוּא מַאֲכִילָהּ כְּמוֹ שֶׁהֶאֱכִילָהּ אָבִיו:
כסף משנה
19.
[Similar laws apply when] a daughter of an Israelite marries an Israelite first and has a son that she bore to him. If she marries a priest [after her first husband dies], she may partake of terumah. If [her second husband, the priest,] dies, but she bore him a son, she may partake [of terumah] by virtue of the son [she bore him]. For he enables her to partake of terumah as his father did.61Similarly, if her son conceived by the priest fathers children, she may continue to eat by virtue of them, even if her son dies. If, however, the son conceived by the priest dies childless (or he and his descendants die), she may no longer partake of terumah.

זרעים הלכות תרומות פרק ו
Zeraim Terumos Chapter 6