If a kohen marries a woman who is not from a family of kohanim, once she becomes a member of his household she will be permitted to eat teruma in his home. Were he to die, assuming that they had children together, she will continue to eat teruma, since the children allow her to remain in her late husband’s household. If she was pregnant at the time of her husband’s death, one opinion in the Mishna suggests that the family slaves cannot eat teruma, since they are partially owned by the unborn child – who does not have the ability to feed them.
When Rabbi Yishmael the son of Rabbi Yose quotes his father as ruling that in such a case a daughter has the ability to allow the slaves to eat, but a son does not, Abaye explains that this is talking about a very specific case, when there is not enough money in the estate for the daughters to be supported if the sons were to take their inheritance. In such a case the sons will receive nothing, and even if the unborn child is a son, he will not have rights to the slave and therefore cannot keep him from eating teruma.
According to the Torah, when a man dies it is his sons who will receive the inheritance from him, while the daughters will receive nothing. Only if there are no sons and there are daughters will the daughters receive the inheritance. However, the Sages established a clause in the ketuba (the marriage contract) guaranteeing that the daughters will be supported by the estate until they either marry or reach maturity. Given the fact that the ketuba is viewed by the halakha as a promissory note, it has the status of a bill or obligation and it must be paid out before the sons collect their share of the inheritance. Thus, if there are limited funds, it is the daughters who will be supported, while the sons will not receive even minimal support from the estate. Even so, there remains a possibility that the sons will sell the property of the estate, and since on a biblical level it belongs to them the sale will take effect, depriving the daughters of their means of support.