Horayot, Chapter Three, Mishnah One
In the case discussed by our mishnah, a high priest or king issued an errant ruling that was subsequently followed by the people, but before they could bring the appropriate sin-offering, they lost their office. The question is, are they still obligated to bring the same offering, even though they are no longer high priest or king.
As a background to this mishnah, I should point out that the removal of high priests and kings from their office was not an uncommon occurrence in the Second Temple period. Due to the political pressures of the Roman rulers, kings and especially high priests were often replaced.
If an anointed priest transgressed and afterwards relinquished his high priesthood, and similarly if a ruler transgressed and afterwards relinquished his reign, the anointed priest brings a bullock, and the ruler brings a he-goat.
The mishnah rules that in the situation where the high priest or king issued an errant ruling but were removed from office before bringing their sin-offering, they still bring the same sin-offering that they would have brought had they still been in office. The obligation for the offering is set at the time of the errant ruling, and not at the time of the bringing of the sacrifice. Therefore, the high priest still brings a bull, and the king still brings a goat.
In the next mishnah we will see that the high priest brings a bull even if he issued the errant ruling after he was removed from office. Therefore, our mishnah is not really necessary with regard to the high priest because he in any case brings a bull. The only reason that the mishnah teaches about the high priest is because it wants to teach about the ruler, who brings a goat only if he issues the errant ruling while still a king.