One of the key distinctions between the land of Israel and the Diaspora is the ability to observe the many mitzvot between man and the land. The seventh chapter of Yevamot focuses on the intricacies of the laws of terumah, which may be eaten only by a kohen or a member of his household. The chapter begins by analyzing the case of a kohen marrying someone prohibited to him, such as a divorcee. While such a woman may not eat terumah--a forbidden woman cannot be truly part of the household--her servants who accompany her might be able to do so.
The extension of the right to eat terumah to the (non-kohen) wife of a kohen applies only as long as the couple is married. Upon divorce or her husband's death, she would no longer be allowed to eat terumah. As a corollary to this, a bat-kohen, daughter of a kohen who marries a non-kohen is forbidden to eat terumah, but upon the dissolution of her marriage she "returns to the house of her father" and would once again be permitted to eat terumah.
The above holds true only in the absence of children. If the couple have children, then the death of the husband has no impact on the widow's right to eat terumah. The widow of the kohen would continue to eat terumah on the "strength" of her child, and the daughter of a kohen widowed from a non-kohen would remain prohibited from doing so because of her child.
Interestingly, such holds true even if the child is a mamzer, an illegitimate child. The Mishnah (Yevamot 69b) gives the following example: a bat-kohen marries a non-kohen, and they have a daughter who marries a non-Jew and produces a child. Both the husband (the grandfather) and daughter die, leaving this bat-kohen and her grandson who has, according to the Mishnah, the status of mamzer. Nonetheless, this mamzer, as a descendant of a non-kohen, prevents his grandmother from eating terumah. Had the widow been someone married to a kohen, her mamzer grandson would allow her to continue to eat terumah.
While having a mamzer as a grandchild may allow one to eat terumah, having a grandson who is a kohen gadol may do the exact opposite. Such occurs when a bat-kohen marries a non-kohen and they have a daughter. This bat-kohen can no longer eat terumah. However, if and when their daughter marries a kohen, she may eat terumah. And this daughter can have a son who can become the kohen gadol. Even after the (non-kohen) daughter is widowed, she may continue to eat terumah,as she has a son who is a kohen. However, the grandmother who is herself akohen(et), who was married to a non-kohen is not allowed to eat terumah because of her kohen gadol grandson. The Mishnah concludes with the grandmother saying, 'There should be few like my [grand]son, who deprives me of eating terumah' (Yevamot 69b).
This discussion may seem a little strange. Why should it be so important that one be able to eat terumah? All who may eat terumah may also eat non-terumah food. And eating such regular food would seem so much easier! One need not worry about impurity, whereas one who eats terumah in a state of impurity is punished with "death at the hands of heaven", and even if done inadvertently, must pay a 20% fine of the amount eaten.
Eating terumah carries with it a certain amount of risk. But risk is part and parcel of all that is holy. One cannot grow if one does not take chances. It is a privilege to eat sanctified food. Sadly, the privilege of eating terumah no longer exists, and even under optimal conditions, it may only be eaten by a kohen and his family. Yet today we all have the zechut, the tremendous opportunity, to eat food sanctified with the holiness of the shmitta year. Many are afraid to eat such foods, nervous about the technical details of such and the care that must be taken. But after 2,000 years, we have merited to be able to eat such food--to imbue our pallets with the holiness of the land. And one need not be a kohen to eat such. All one has to do is go shopping in Israel and purchase those foods endowed with the sweet taste of shmitta.
 Thankfully, Jewish law does not accept the ruling of this Mishnah, concluding that a mamzer only comes about through adultery, and not through intermarriage.