Gemara

(Mishnah): If Reuven made a Shali'ach to give a Get, (even) if he was old or sick, the Shali'ach gives the Get. We rely on the Chazakah that Reuven is still alive.

A Bas Yisrael married to a Kohen eats Terumah even when he goes abroad. We rely on the Chazakah that he is still alive. If Shimon sent a Chatas from abroad, we rely on the Chazakah that he is still alive, and we offer it on the Mizbe'ach.

(Gemara - Rava): This is only if Shimon was less than 80 years old, and only moderately sick. If he was at least 80, or was Goses (a dying person who probably will not survive), we are concerned lest he died.

Question (Abaye - Beraisa #1): If Reuven made a Shali'ach to give a Get, (even) if Reuven was 100 years old, the Shali'ach gives the Get. We rely on the Chazakah that Reuven is still alive.

Version #1: Rava is refuted.

Version #2: Rava is not refuted. Perhaps we are concerned that a person in his 80's may die any day; but once one lived to 100 we are not concerned.

Question: The Mishnah allows a Kohen's wife to eat Terumah when he is abroad. We rely on the Chazakah that he is still alive;

Contradiction (Beraisa #2): If a Kohen gave a Get to take effect 'just before I die', his wife is immediately forbidden to eat Terumah, lest he die right away.

Answer #1 (Abaye): Our Mishnah is R. Meir, who is not concerned lest someone die. The Beraisa is R. Yehudah, who is concerned:

(Beraisa - R. Meir): If one bought wine from Kusim (and cannot tithe it now), he says 'the two Lugim that I will later separate should be Terumah...', and he may drink immediately;

R. Yehudah and R. Yosi require separating the tithes before drinking.

A Beraisa says that they forbid relying on Breirah lest the barrel break before he tithes it, and retroactively, what he drank was Tevel. The concern lest the barrel break is like the concern lest a man die!

Answer #2 (Rava): We are not concerned lest her husband already died. Tana'im argue about whether or not we are concerned (lest a barrel break, which is like concern) lest he will die (in the next moment, and she is already divorced).

Rishonim

Rif and Rosh (Gitin 14a and 3:4): We give the Get if Reuven was old or sick, relying on the Chazakah that Reuven is still alive, for most sick people recover. We do not give it if he was Goses, for most Gosesim die.

Ran (DH v'Davka): The Rif rules like the first version, that we refuted Rava's teaching that we do not rely on the Chazakah if someone is in their 80's.

Korban Nesan'el (30): The Ramah argues, and says that someone between 80 and 100 is like a Goses. Rashi says that someone who reached 90 is already extraordinary, so we are not concerned lest he died.

Rambam (Hilchos Gerushin 6:28): If a Shali'ach brought a Get and when he left Reuven was old or sick, we give it to her, relying on the Chazakah that Reuven is alive. It if he was Goses, most Gosesim die, so even if he gave it to her she is Safek divorced, for a Get after death is invalid.

Magid Mishnah: Even if Reuven had died, she could remarry to a Yisrael unless it is a situation of Yibum. The Chazakah that he is alive permits even in a situation of Yibum, and forbids her to a Kohen.

Note: There are other differences. A woman who was widowed once (some say, even twice) may remarry if she was divorced, but it is dangerous to marry a woman widowed two (or three) times (Yevamos 64b).

Magid Mishnah: The Rif and Rambam rule like the simple understanding of the Beraisa, which does not distinguish whether or not the Shali'ach was over 80. The Yerushalmi supports this.

Hagahos Maimoniyos (9): Avi ha'Ezri is stringent like Rava (we are concerned if the husband was at least 80).

Rosh (Kidushin 3:16): Rashi says that a Goses cannot give a gift. R. Chananel explains that it is as if he is dead. R. Yo'el derived that a Goses cannot divorce even if his mind is settled, for it says "v'Nosan", and he cannot give. The Ri proves that he can divorce from Gitin 28a. We do not give a Get sent by a Goses because most Gosesim die. If we knew that he was alive, we would give it!

Poskim

Shulchan Aruch (EH 141:68): If Reuven's Shali'ach brought a Get, he gives it to her relying on the Chazakah that Reuven is alive, even if he was old or sick when he left him.

Rema: Some say that this is only if he was naturally sick. If he was wounded and became Tereifah, the law of a Goses applies to him.

Shulchan Aruch (ibid.): If Reuven was Goses when he left him, he should not give it, for most Gosesim die. If he gave it to her she is Safek divorced.

Beis Shmuel (105): Only a Goses who can talk can divorce. If he cannot speak now, even though he could speak when he gave the Get to the Shali'ach, we are concerned that he lost sanity, for a Goses must be checked. However, we could say that if he could speak and was sound-minded when he gave the Get, and later he became mute, he need not be checked, since he was Goses and settled.

Bach (DH u'Mah she'Chosav): Rashi and R. Chananel say that a Goses cannot divorce. How can a Shali'ach can give a Get when the husband is Goses? We must say that he became Goses after sending the Get.

Rebuttal (Beis Shmuel 105): In such a case we would not let the Shali'ach give the Get, out of concern lest he lost sanity.

Beis Shmuel (106 and Maharshach 2:39): The Magid Mishneh (Hilchos Gerushin 6:29) says that we do not give a Get (if there is a Safek that her husband died) to make her a Safek divorcee. This is reasonable in a situation of Yibum, lest she err and think that the Get was valid, and remarry without Chalitzah (and really, she fell to Yibum). If she cannot fall to Yibum, why shouldn't she receive a Get to permit her to marry a Yisrael?

Maharshach (ibid.): Chachamim forbade to do Chalitzah mi'Safek, lest later she learn that the Chalitzah was unnecessary, marry a Kohen, and people will think that a Kohen married a Chalutzah. A Shali'ach may give a Get mi'Safek, for once he received the Get her Heter to Kehunah was in Safek.

Note: Also, the Isur of Chalitzah is only mid'Rabanan, so there is concern lest people think that Chachamim permitted a Chalutzah to a Kohen. Surely, people will not think that Chachamim permitted a divorcee to a Kohen!

Shulchan Aruch (ibid.): Some say that the Heter to give it when Reuven was old is only if he was less than 80 (Rema - or more than 100), but if he was between 80 and 100, he is like a Goses.

Beis Yosef (DH u'Mah she'Chosav uv'Chezkas): The Rashba says that the Halachah follows Abaye, like the Stam Mishnah and Beraisa, and Yerushalmi. The Gemara answered for Rabah, but we do not rely on this. The Rif, Rosh and Rambam did not bring Rabah's opinion. The Rashba says that the Yerushalmi supports this. The Ramah is stringent like Rabah according to the simple reading of the Gemara, i.e. between 80 and 100. Rashi said that Rabah is stringent only until 90. Also Avi ha'Ezri is stringent.