We now move to Mishnah 2 in the third chapter, which deals with two cases: an anointed kohen who has left his anointed office, and a nasi who has left his position of greatness, both of whom sinned after their term of office had ended.
An anointed kohen who has left his anointed office:
A Kohen Gadol who served in his office and then ceased to fill it - he developed a permanent blemish, became tamei, or grew too old to serve - and afterwards he sinned. That is, at a time when he is no longer the acting Kohen Gadol, he committed a transgression for which he would have brought the bull of an anointed kohen had he been the acting Kohen Gadol: he issued a ruling for himself, and acted on his ruling in a transgression whose penalty is a fixed sin offering.
A nasi who has left his position of greatness:
"V'chein hanasi she'avar migdulaso v'achar kach chata" - a king who no longer functions as king, and who, as an ordinary person, transgressed a prohibition that obligates him to bring a sin offering.
The ruling of the Mishnah in both cases:
"Kohen Mashiach mevi par" - the anointed kohen brings the bull of an anointed kohen just as before, because once a person becomes a Kohen Gadol he remains a Kohen Gadol forever. He does not lose his sanctity, even though he no longer functions as Kohen Gadol.
"V'nasi k'hedyot" - no sanctity is conferred upon a king, and from the moment he is no longer king he is like an ordinary person. Therefore the nasi brings the very same sin offering that an ordinary person brings: a female goat or a female sheep.
A precise reading of the word "v'chein":
A careful reading of the Mishnah raises a difficulty. The word "v'chein" ("and likewise") indicates that the same principle applies in both cases, whereas in fact the Mishnah teaches that the Kohen Gadol brings his usual offering, while the king who is no longer king brings a different offering. If so, there is no "likewise" here at all, and the two rulings are not similar to one another.
Tosfos HaRash addresses this and answers that the word "v'chein" was used only in order to parallel the previous Mishnah, as an aid to memory. In any case, this "v'chein" is not to be taken at face value, since the difference between the two rulings is enormous.
In summary: In this Mishnah we learned the law of an anointed kohen who has left his anointed office and a nasi who has left his position of greatness, both of whom sinned after their term of office ended: the anointed kohen brings a bull, since the sanctity of the Kohen Gadol never leaves him; whereas the nasi is treated like an ordinary person and brings a female goat or a female sheep, since no sanctity is conferred upon a king. We also examined the precise wording "v'chein" and the answer of Tosfos HaRash, that this wording was used merely for the sake of the parallel.