Zevachim 71 - Animal Mix-Up
There are five cases when a sin-offering cannot be brought, cannot be left to graze, and has to die. One of these cases is when the owner of the sacrifice died. Since the sacrifice is only brought to atone for his misdeed, and there is no atonement after death, such sacrifice cannot be brought. Furthermore, it cannot be left to graze until it develops a blemish which would allow to redeem it - which is a usual solution in such circumstances. Instead, it is left confined in a cell without food. The other cases include consecration by exchange, an offspring of a sin-offering, the owner being atoned for with another animal, and an animal that is older than one year.
If any of these doomed animals got mixed-up with other sacrifices - even if only one became mixed with ten thousand - they must all be left to die. The root cause of it is that this sacrifice is forbidden for all benefit, and thus measures need to be taken to avoid possible transgression. The law about five cases of a sin-offering is in the category of laws that were taught to Moses on Sinai and cannot be derived from the Torah.
Art: Rembrandt Van Rijn - Dead Peacocks