Gittin, Chapter 3, Mishnah 4. In the previous mishnah we dealt with the concept of chazakah - the presumption that a person is still alive for various areas of halachah. Our mishnah continues with that same subject and expands it.
"Sheloshah devarim amar Rabbi Elazar ben Perata lifnei chachamim, v'kiyemu es devarav" - Rabbi Elazar ben Perata said three things before the Sages, and they upheld his position and agreed with him.
The three situations in which a person remains presumed alive:
"Al ir shehikifah karkom" - a city surrounded by a military siege.
"V'al hasefinah hamitarefes bayam" - a ship struggling at sea to stay afloat.
"V'al hayotzei lidon" - a person going to court for a capital offense, who may be executed as a result of the verdict. But he has not yet been executed, and the verdict has not even been issued; he is merely on his way to stand trial for it.
In these three situations - "shehen b'chezkas kayamin" - we may assume that they are still alive. For example, if the man is a kohen, his wife continues to eat Terumah, and so on.
In contrast, three situations in which the presumption no longer holds:
"Ir shekevashah karkom" - a city that has already been captured by the siege, the enemy having succeeded in taking it over.
"U'sefinah she'avdah bayam" - a ship that has already sunk.
"V'hayotzei lehareig" - one whose verdict has already been handed down and who has been declared guilty, and is being led out to execution.
Regarding these the mishnah says: "Nosnin aleihen chumrei chaim v'chumrei mesim" - we must be stringent both because of the possibility that they are alive and because of the possibility that they are dead.
Here is how this plays out in practice:
A daughter of an ordinary Israelite married to a kohen: she eats Terumah only as long as her husband is alive, so we do not permit her to eat Terumah because of the possibility that he has already died - this is the stringency of treating him as dead.
A daughter of a kohen married to an ordinary Israelite: if he had died, she would return to eating Terumah provided she has no children from him; but if he is still alive, she may not eat Terumah - this is the stringency of treating him as alive.
The result is that in both cases - "lo sochal biterumah" - she may not eat Terumah, because we are stringent both for the possibility that he is alive and for the possibility that he is no longer alive.
In summary: in this mishnah we learned the three things that Rabbi Elazar ben Perata said before the Sages, and they upheld his words: a city surrounded by a siege, a ship struggling at sea, and one going out to stand trial - these are presumed alive; and in contrast, a city captured by a siege, a ship that sank at sea, and one being led out to execution - regarding whom we apply the stringencies of the living and the stringencies of the dead, and therefore both the daughter of an Israelite married to a kohen and the daughter of a kohen married to an Israelite may not eat Terumah.