Bamidbar 35:25 - 27 state that a person who inadvertantly kills someone must reside in the city of refuge until the Kohen Gadol dies. If that person leaves the refuge city, the "Go'el Hadam" (loose translation - "blood avenger") can kill the other person.
Suppose that after the Cohen Gadol dies, the indavertent killer decided to live in the refuge city, or, for that matter, go to one of the other 5 (there were 6 in total.) Can the Go'el Hadam kill him and be innocent?
In summary, when the Cohen Gadol dies, is the protection eliminated? If the protection is NOT eliminated, does he have to stay in the original refuge city (I state this because verse 25 uses the term "ir miklaTO" meaning HIS refuge city. Perhaps, a gemarrah uses this term for some point?) or can he go to another one?