Gemara

(Beraisa - R. Yehudah): In the Mikdash there was not a box (in which people would leave money) for (Kohanim to buy and offer) Kinei Chovah (Olas ha'Of and Chatas ha'Of), because of mixture.

Question: What does this mean?

58b - Answer (Chachamim of Eretz Yisrael): We could not offer them, because we must be concerned lest a contributor (of money in the box) died.

Objection: We are not concerned for this!

(Mishnah): If one sent a Chatas from abroad, we rely on the Chazakah that he is still alive, and we offer it on the Mizbe'ach.

Answer #2: Rather, we must be concerned lest we learn that a contributor died, for then we could not offer any of them,

Gitin 28a - Mishnah: If Reuven made a Shali'ach to give a Get, (even) if Reuven was old or sick, the Shali'ach gives the Get. We rely on the Chazakah that Reuven is still alive. Likewise, if one sent a Chatas from abroad, we rely on Chazakah and we offer it.

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

Question (Abaye - Beraisa): 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 (we see that he is extraordinary).

Mishnah: If one sent a Chatas from abroad...

Question: He must personally come to do Semichah (press on the animal's neck)!

Answer #1 (Rav Yosef): The case is, a woman sent it (women do not do Semichah).

Answer #2 (Rav Papa): The case is, he sent Chatas ha'Of (Semichah does not apply to birds).

Rishonim

Rif (Gitin 14a) and Rosh (Gitin 3:4): A Shali'ach may give a Get, (even) if the Meshale'ach was old or sick. We rely on the Chazakah that the Meshale'ach is still alive. This is only if he was (normally) sick, for most sick people recover, but not if he was Goses, for most Gosesim die.

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

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.

Question: The Gemara asserted that we are not concerned for death. We should be concerned lest one of the contributors was over 80, for then we are concerned!

Answer #1 (Tosfos Yoma 55b DH veha'Tanan): This is not common, we need not be concerned for it.

Note: Once, (because of great demand) the price of birds skyrocketed. R. Shimon ben Gamliel expounded that a woman with five definite births or Zivos brings one Korban and may eat Kodshim. The price plummeted that same day (Kerisus 8a). This shows that Most Kinei Chovah offered were for Zivah or Yoledes. Normally, these do not apply to women above 80.

Answer #2 Tosfos (ibid.): It is a stringency of Get to be concerned for death after 80. This is why Rava taught his law regarding Get, and not regarding Chatas.

Rambam (Hilchos Girushin 6:28): (Even) if the husband was old or sick, his Shali'ach gives the Get and we rely on the Chazakah that the husband is still alive. However, if he was Goses it is Safek Girushin.

Magid Mishnah: The Rif and Rambam rule like the simple understanding of the Beraisa, which does not distinguish whether or not the Meshale'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).

Rambam (Hilchos Pesulei ha'Mukdashim 4:14): If one sent a Chatas from abroad, we rely on the Chazakah that he is still alive, and we offer it. This refers to Chatas ha'Of, or Chatas Behemah of a woman, which do not require Semichah.

Question (Lechem Mishneh Girushin 6:28): Why doesn't the Rambam distinguish whether or not the sender was Goses, like he distinguishes regarding Get and Terumah? If he relies on what he wrote there, he should have written the law in only one place, and we would learn both other places from there!

Answer #1 (Mishneh l'Melech): The Rambam does not distinguish whether or not the Meshale'ach was Goses. This is like Tosfos (Yoma 55b DH veha'Tanan), who says that the concern for death for someone above 80 is a stringency of Get; the same applies to Goses. However, most Gosesim die, so it is difficult to say that we are not concerned for death! Rather, Rava taught that both concerns apply to Get, but regarding Chatas we are concerned only for Goses. The Rambam forbids the wife of a Goses Kohen to eat Terumah when her husband is away; we cannot say we are more stringent about Terumah than Kodshim! It appears that the Rambam relied on what he wrote in Hilchos Girushin and Hilchos Terumos that we are concerned lest a Goses died.

Answer #2 (Kesav Sofer Gitin 28b DH u'Tzrichah): The Rambam holds that nowadays Terumah is mid'Rabanan. Since we rely on the Chazakah for Get mid'Oraisa, he did not need to say that we rely on it for Terumah mid'Rabanan. Regarding Terumah he said that we are concerned that a Goses died, so he did not need to say that we are concerned regarding Kodshim mid'Oraisa.

Keren Orah (Menachos 62 Tosfos DH v'Chen): Perhaps Semichah is Me'akev Chatas more than other Korbanos, because Chatas is primarily for Kaparah.