If the anointed priest was deposed from his (high-) priesthood and then he sinned; and, similarly, if a king was deposed from his kingship and then he sinned — the anointed priest brings a bullock [Even though he does not officiate he remains in his sanctity; for there is no difference between an officiating (high-) priest and a deposed (high-priest) but the (Yom Kippur) service and the Yom Kippur bullock and the tenth of the ephah, that is offered each day (as stated below), but a Nassi, once he has been deposed, is considered a commoner], and the Nassi is like a commoner.
Bartenura on Mishnah Horayot
כהן משיח שעבר ממשיחותו וכו' – even though he does not perform [the Divine Service], he still remains in his holiness, for there is no difference between a Kohen who serves and a Kohen who has passed from service, other than the Divine Service and the bullock of Yom Kippur and one-tenth of an ephah that he offers on each day, as is mentioned further on (see Mishnah Horayot, Chapter 3, Mishnah 4; see also Mishnah Megillah, Chapter 1, the end of Mishnah 9).
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English Explanation of Mishnah Horayot
Introduction
Mishnah two teaches the halakhah regarding a high priest or king who issue an errant ruling after having relinquished their office.
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English Explanation of Mishnah Horayot
If the anointed priest relinquished his high priesthood and afterwards transgressed, and similarly if a ruler relinquished his reign and afterwards transgressed, the anointed priest brings a bull while the ruler is like a regular person. When the high priest is removed from office, he does not lose his sacred status (we will discuss this below in mishnah four). Therefore, even if he issues an errant ruling after having been removed, he is still considered like a high priest, and he brings a bull. However, the king does lose his status, and is therefore treated like a regular person who unwittingly sins and brings a she-goat or female sheep.
