The Torah commands in Parashat Emor (Vayikra 22:12) that a Kohen’s daughter, who is normally permitted to eat her father’s hallowed food, forfeits this privilege if she has a relationship with an “Ish Zar” – literally, “a foreign man.”
This is understood as referring to two different situations. First, it speaks of a Kohen’s daughter who has a relationship with somebody with whom relations are forbidden, in which case she becomes a “Halala” – meaning, she loses her priestly status entirely. She may not ever marry a Kohen, or partake of either Teruma (the portion of agricultural produce given to a Kohen) or Kodashim (the portions of sacrifices which a Kohen may share with his family). Secondly, this verse speaks of a Kohen’s daughter who marries a non-Kohen. Even though this marriage is entirely permissible, nevertheless, she is not permitted to eat Teruma or Kodashim as long as she is married to the non-Kohen. If she is widowed or divorced, and she has no children from the non-Kohen, then she may once again eat her father’s Teruma, but even then, she remains forbidden from eating Kodashim.
The Sefer Ha’hinuch writes that this prohibition applies in all places, and when Teruma is required on the level of Torah obligation. If a Kohen’s daughter ate Teruma or Kodashim after having had an illicit relationship, or while married to a non-Kohen, or if she ate Kodashim even after being widowed or divorced by a non-Kohen, then she is liable to Malkut.
The Minhat Hinuch notes that the punishment for this transgression is Malkut, and not Mita Bi’ydeh Shamayim (death at the hand of G-d, as opposed by court execution). We might have assumed that the woman in this case should be treated like a “Zar” – a non-Kohen, who is liable to Mita Bi’ydeh Shamayim for eating Teruma. Instead, she is liable to the less stringent punishment of Malkut. The Minhat Hinuch explains that since the woman in this case originally was allowed to eat Teruma and Kodashim, her status differs from that of a full-fledged “Zar,” who was never permitted to eat hallowed food. As such, her transgression is less severe than that of a “Zar” who partakes of Teruma or Kodashim.
On the basis of this analysis, the Minhat Hinuch establishes that if a Kohen married a woman forbidden for Kohanim, such as a divorcee, the daughter produced by this marriage would be liable to Mita Bi’ydeh Shamayim for eating Teruma or Kodashim. She is a “Halala” from birth, and was never allowed to eat Teruma, as opposed to a woman who was permitted to eat Teruma and then became a “Halala” due to a forbidden relationship. Therefore, her status is that of a full-fledged “Zar,” and not that of a Kohen’s daughter who later became a “Halala.” As such, she would be liable to the severe punishment of Mita Bi’ydeh Shamayim, just like a “Zar.”