Before us is Mishnah 3 in chapter 6 of Maseches Yevamos, which deals with a woman who was betrothed to a kohen in a marriage forbidden to him, and with the question of whether she may still eat Terumah in her father's house.
The opening clause of the Mishnah:
"Almanah l'kohen gadol, gerushah v'chalutzah l'kohen hedyot, min ha'eirusin - lo yochlu bi'Terumah" - a widow married to a Kohen Gadol, and a divorcee or a chalutzah married to an ordinary kohen, from betrothal alone, may not eat Terumah. The Mishnah deals with two cases:
A widow to a Kohen Gadol - a widow who married a Kohen Gadol, who is forbidden to him.
A divorcee or a chalutzah to an ordinary kohen - a divorcee or a chalutzah who married an ordinary kohen, who are forbidden to him.
In both cases the betrothal takes effect, and the Mishnah is discussing a situation in which the bond between them rests on betrothal alone, that is, on kiddushin without marriage.
The difficulty in this ruling:
At first glance, the daughter of a kohen who becomes betrothed is disqualified from eating Terumah in her father's house only when she was betrothed to someone who is not a kohen; here, however, she was betrothed to a kohen. True, she is not permitted to marry him, since this is a forbidden marriage, but by rights she should still be allowed to eat Terumah in her father's house.
However, since this is a betrothal of transgression, the assumption is that the relationship will eventually be consummated through an act that will disqualify her. For that reason, already from the moment of betrothal she has the status of one who is 'waiting for cohabitation' - waiting for the next stage, at which she will be disqualified - and therefore even at this stage itself she is disqualified from eating Terumah in her father's house.
The opinion of Rabbi Elazar ben Rabbi Shimon:
Rabbi Elazar ben Rabbi Shimon rules that she remains fit. In his view she is not disqualified from eating Terumah at this stage, but only after the marriage actually takes place and there is cohabitation that renders her a chalalah. Until that point she is not disqualified at all.
"Nis'almenu o nisgarshu":
The Mishnah continues and discusses a case in which the relationship came to an end - whether the husband died or whether he divorced her, whether the husband was a mamzer, a Kohen Gadol, or an ordinary kohen. Ordinarily, the daughter of a kohen who is widowed or divorced returns to eating Terumah in her father's house, but here a distinction must be drawn:
"Min ha'nisu'in - pesulos" - if the death or the divorce occurred after the marriage, they have already become chalalos and have been disqualified from Terumah through the cohabitation that took place at the time of the marriage, and they can no longer eat Terumah.
"Min ha'eirusin - kesheros" - if they were widowed or divorced after there had been betrothal alone, they remain fit. In this case even the first Tanna agrees that they are not disqualified, since the entire reason for the disqualification in the opening clause was that they were waiting for the disqualifying cohabitation; and here, once the relationship has ended, the disqualification never occurred and never will occur, and therefore even according to the first Tanna they are fit to eat Terumah in their father's house.
In summary: we have learned that a widow betrothed to a Kohen Gadol, and a divorcee or a chalutzah betrothed to an ordinary kohen, are disqualified from Terumah already from the time of betrothal, because they are waiting for the disqualifying cohabitation, while Rabbi Elazar ben Rabbi Shimon rules them fit until cohabitation actually takes place. We have also learned that once they were widowed or divorced, if this was after marriage they are disqualified, since they have already become chalalos, and if it was after betrothal alone they remain fit, since the disqualification neither occurred nor will occur.