Gemara

(Mishnah): If an animal was found (in any direction) outside Yerushalayim, no further than the distance from Yerushalayim to Migdal Eder, if it is a male, it is (treated like) an Olah. If it is a female, it is (treated like) a Shelamim.

(R. Oshaya): The case is, the finder accepts on himself to bring the Korban that the one who lost the animal needed to bring.

Pesachim 62a: An Arel or Tamei can send a Korban through a Shali'ach, except for Korban Pesach (for one must be able to eat the Pesach).

Zevachim 74b (Mishnah): If Kodshim became mixed with Kodshim, if all are the same Zevach (Chatas or Olah...), each is offered l'Shem its owner.

Question: The owner must do Semichah (press on the neck of his Korban)!

Answer (Rav Yosef): The Mishnah discusses Korbanos of women (they do not do Semichah).

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 Chezkas Chai (we assume that Reuven is still alive). If one sent a Chatas from abroad, we rely on Chezkas Chai, and we offer it on the Mizbe'ach.

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 one made a Shali'ach to give a Get, if he was 100 years old, the Shali'ach gives the Get. We rely on Chezkas Chai.

Version #1: Rava is refuted.

Version #2: Rava is not refuted. Perhaps we are concerned that one in his 80's may die; but we are not concerned for one over 100 (he is extraordinary).

Question: The owner of the Korban must personally come to do Semichah!

Answer #1 (Rav Yosef): The case is, a woman sent it.

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

Yoma 55b (Beraisa - R. Yehudah): In the Mikdash there was no box (to leave money) for (Kohanim to buy and offer) Kinei Chovah (Olas ha'Of and Chatas ha'Of), due to mixture (lest a contributor, die, and then we could not offer them).

58b - Question (Mishnah): If one sent a Chatas, we rely on Chezkas Chai.

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

Rishonim

Rif and Rosh (Gitin 14a and 3:4): A Shali'ach may give a Get, (even) if the Meshale'ach was old or sick, 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 Chezkas Chai for one in his 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 in Yoma said that we are not concerned for death. Perhaps one of the contributors was over 80, and we should be concerned!

Answer (Tosfos Yoma 55b DH veha'Tanan): This is rare, we are not concerned for it. Alternatively, 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.

Note: Once, due to great demand, the price of birds skyrocketed. R. Shimon ben Gamliel expounded a leniency for women who needed to bring birds for births or Zivah, and the price plummeted (Kerisus 8a). This shows that most birds were for birth or Zivah. These rarely apply to women above 80.

Rambam (Hilchos Girushin 6:28): (Even) if the husband was old or sick, we rely on Chezkas Chai. If he was Goses it is Safek Girushin, for most Gosesim die.

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.

Rambam (Hilchos Pesulei ha'Mukdashim 4:14): If one sent a Chatas, we rely on Chezkas Chai, and we offer it on the Mizbe'ach. This refers to Chatas ha'Of, or Chatas Behemah of a woman, which do not require Semichah.

Question (Lechem Mishneh Girushin 6:28): The Rambam should teach that we do not rely on Chezkas Chai if the sender was Goses, like he says about 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 sender was Goses. Tosfos (Yoma 55b DH veha'Tanan) says that the concern for death for one above 80 is a stringency of Get; the same applies to Goses. This is difficult. Most Gosesim die. We should be concerned for death! Rather, Rava taught that both concerns apply to Get; for Chatas, we are concerned only for Goses. When a Goses Kohen is away, the Rambam forbids his wife to eat Terumah. We cannot be 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, and surely for Terumah mid'Rabanan! We do not rely on the Chazakah for a Goses for Terumah, and surely not for Kodshim mid'Oraisa!

Question (Aruch ha'Shulchan ha'Asid Kodshim 68:8): The Rambam holds that even though Semichah is not Me'akev, one may not send a Korban that requires Semichah, even if he lives far away and cannot do Semichah. In Hilchos Bi'as Makdish 2:12) he allows an Arel or Tamei to send any Korban except for Pesach! Indeed, the Gemara (Pesachim 62a) says so, but Tosfos (DH Arel) establishes it to discuss birds, Bechor or Ma'aser which do not require Semichah. The Rambam did not distinguish!

Answer (Aruch ha'Shulchan, ibid.): The Rambam holds that Semichah is Me'akev only if the owner could do Semichah, e.g. when he is far away. When the Torah forbids him, e.g. Arel or Tamei, it is not Me'akev.

Question: It is more reasonable that it is Me'akev when the Torah forbids him, just like Bilah (mixing a Minchah with oil) is Me'akev when it is impossible!

Answer (Aruch ha'Shulchan, ibid.): Tosfos (Zevachim 75a DH v'Ha) proves that this does not apply here. It is reasonable for Bilah (or a similar Avodah) to be Me'akev, for it is a Pesul in the Korban itself, but Semichah is not.

Rambam (Hilchos Bi'as Makdish 2:12): An Arel or Tamei (who can immerse, and be totally Tahor at night) may send a Korban and we offer it

Aruch ha'Shulchan ha'Asid (Kodshim 68:9): The Rambam allow an Arel or Tamei to send Korbanos except for Pesach, and we offer it for him. We do not offer for one who is Tamei Mes until he becomes Tahor.

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