Today's "Daf Yomi" folio is folio 12 from the Babylonian Talmud tractate Yoma which deals with Yom Kippur. The discussion here takes up one of the issues from the first mishnah of the chapter, the appointment of a substitute high priest in case the high priest becomes impure and is unable to perform the Yom Kippur sacrifices.
So what happens if the substitute takes over from the high priest on the Day of Atonement?
"The rabbis taught: When the high-priest happened to become unfit for service, and his substitute performed it, then after the Day of Atonement the high-priest resumes his service, and all the laws regarding the high-priesthood apply to the substitute (he can no longer be like a common priest). Such is the decree of R. Meir. R. Jose, however, says: The high-priest resumes his service, the substitute does not become like a high-priest, nor continues to be as a common priest. And R. Jose added: It happened to Joseph b. Alem of Ziporeth, that he was a substitute for the high-priest, who performed the service instead of the high-priest, to whom an accident had happened. Later the sages said, the high-priest should resume his service, and that Joseph b. Alem is fit no longer to be either a high-priest or a common priest. A high-priest, to prevent enmity; and a common priest, because there is a rule, in holiness one may increase but not decrease. Said Rabba bar bar Hana in the name of R. Johanan: The Halakha prevails according to R. Jose. R. Jose grants, that if the substitute has performed service in the Temple, this service is valid.
R. Jehudah said in the name of Rabh also: The Halakha prevails according to R. Jose, and R. Jose grants that when it happens the high-priest dies, he may become high-priest. This is self-evident? One might say, since he was his rival in life, he might not become a high-priest after his death. He comes to teach us it is not so."
(BT Yoma 12b-13a; translation by Radkinson from Internet Sacred Text Archive; I've never heard of this translation but it seems ok and the Soncino translation of Yoma is not available on-line--and needless to say, I'm too lazy to type out my own translation).
Here is how the Daf Yomi page summarizes R. Jose ("Yossi")'s view:
"1. He cannot be a co-Kohen Gadol for fear of enmity.
2. He cannot be a regular Kohen out of respect for his elevated status."
A dubious honor, then, to be chosen as the substitute high priest for Yom Kippur. You can't keep the top job and you can't go back to your old job because you've become over-qualified (at least in terms of holiness).