Bava Kamma 110A

ואם היה זקן או חולה ⁠– נותנה לכל כהן שירצה, ועבודתה ועורה לאנשי משמר.

The baraita continues: And if he was old or sick, so that he cannot perform the Temple service or eat from the offering, he gives it to any priest he wishes to sacrifice it, even to one not on his priestly watch, and performance of its service and its hide are given to the members of the priestly watch.

האי זקן או חולה, היכי דמי? אי דמצי עביד עבודה ⁠– עבודתה ועורה נמי תיהוי דידיה! ואי דלא מצי עביד עבודה ⁠– שליח היכי משוי?

The Talmud clarifies: What are the circumstances of this old or sick priest? If he is in a condition that he is able to perform the Temple service, then performance of its service and its hide should be his as well, as the priest that sacrificed it was acting as his agent. And if he is in a condition that he is not able to perform the Temple service, how can he appoint an agent? The baraita stated that he may give it to any priest he wishes, indicating that he chooses which priest he will appoint as his agent.

אמר רב פפא: שיכול לעשות על ידי הדחק. עבודה ⁠– דכי עביד ליה על ידי הדחק עבודה היא, ומשוי שליח; אכילה ⁠– דכי אכיל על ידי הדחק אכילה גסה היא, ואכילה גסה לאו כלום הוא; משום הכי עבודתה ועורה לאנשי משמר.

Rav Pappa said: The baraita is referring to a case where he is able to do it with difficulty. With regard to the Temple service, where the halakha is that if he performs it with difficulty it is still considered performance of the Temple service, he is therefore able to appoint an agent to do it for him. With regard to eating the offering, where the halakha says that if he eats it with difficulty it is excessive eating, and excessive eating is nothing, i.e., he does not thereby fulfill the mitzva to eat the sacrificial portion, he is not able to appoint an agent to eat it for him. Due to that reason, performance of its service and its hide are given to the members of the priestly watch.