Temurah 6:5-7:1

Temurah 6:5

If an animal is prohibited as a sacrifice, its offspring are still permitted. Rabbi Eliezer says that the offspring of a mortally-wounded (treif) animal may not be offered but the Sages say that it may. Rabbi Chanina ben Antigonos says that a kosher animal that nursed from a treif animal may not be offered. Consecrated animals that develop a mortal injury cannot be redeemed because one cannot redeem consecrated property in order to feed it to dogs (since treif animals can’t be eaten).

Temurah 7:1

Some laws apply to sacrifices but not to Temple upkeep funds; other laws apply to Temple upkeep funds but not to sacrifices. Sacrifices can create temurah, they are subject to piggul (improper intentions), nosar (passing their deadlines) and ritual impurity, their offspring and milk are prohibited after they have been redeemed, one is liable for slaughtering them outside of the Temple courtyard, and one may not give them to craftsmen as wages. None of these laws apply to Temple upkeep funds.