Bamidbar 35:28 "Because he should have remained in the city of his refuge until the death of the high priest; but after the death of the high priest the slayer shall return into the land of his possession."
Rashi
The Cohen Gadol is supposed to enlarge and expand sanctity among the bnei Yisroel. One who kills lessens sanctity (Shabbos 33a). These opposing actions are in conflict and cannot come together. Therefore, the accidental killer is relegated to a city of refuge. Once the Cohen Gadol who presided at the time of the killing is no longer among us, the accidental killer is free to live anywhere.
The Cohen Gadol, the man who has the position of the holiest person, should have prayed that such an accident should not happen. Because he did not pray sufficiently, he is also held responsible for the death. Once he has died there is some amelioration of the sin and the actual killer may go free.
Targum Yonoson ben Uziel
The Cohen Gadol should have prayed on Yom Kippur when in the Holy of Holies that the bnei Yisroel should not stumble in any of the three cardinal sins, including killing someone. If indeed someone kills then the Cohen Gadol will die that year. (If this is so for an accidental killing, all the more so for intentional murder. It is thus surprising that a Cohen Gadol survived for more than a year.)
Chizkuni
The Cohen Gadol is also held accountable for reacting to wrong-doing. If the accidental killer is free to go wherever he wishes, he will appear in front of the Cohen Gadol as well. People will criticize the Cohen Gadol for not taking the law into his own hands and extracting punishment from the accidental killer. He is therefore relegated to a city of refuge and will not appear in front of the Cohen Gadol. Out of sight is out of mind. Once the Cohen Gadol dies, the killer is free to go. People will not hold the new Cohen Gadol to account for a killing that took place when he wasn't even appointed yet.
Rashbam
The accidental killer must flee to a city of refuge. All the cities of refuge were cities designated for the Leviim. The head of the Leviim is the Cohen Gadol, who is also a Levi. He is like a king over these cities. The accidental killers residing in these cities are free to go upon his death, similar to when a king dies and a new one is appointed. He usually frees the criminals in jail to give them a new start under his leadership.
Ralbag
The Cohen Gadol is considered the greatest person of the generation. With the death of a great tzadik, his generation's sins are expiated. The accidental killer is therefore free to leave his city of exile.
Haksav V'hakaboloh
There are no doubt varying degrees of negligence on the part of different accidental killers. They deserve having to be exiled, but for varying lengths of time. Hashem, Who knows exactly how long each person deserves, brings about that each accidental killer does his act at a certain juncture in the Cohen Gadol's life. When the Cohen Gadol dies, one person has been in the city of refuge for a year, another for twenty years, etc. Hashem orchestrates that each person receives his just punishment.
Abarbanel
The death of the Cohen Gadol is such a blow to everyone and sets people into thinking of the ephemeral nature of life. This has a very calming effect on the seething anger experienced by the blood redeemer. The accidental killer is now free to go because the blood avenger will likely not act any more.
Meschech Chochmah
One thinks that the Cohen Gadol was appointed because he in particular was worthy of the position. However, the reason can be a totally different one. Hashem decrees the length of each person's life. As well, He also calculates how long the accidental murderer should have to remain in a city of refuge. It is quite possible that Hashem has decreed that a specific person become Cohen Gadol because the number of years left to his life match with the number of years Hashem wants the accidental murderer to remain in the city of refuge. Thus his remaining in the city of refuge until the death of the Cohen Gadol, "v'yoshav boh ad mose haCohen haGadol," is the cause for this Cohen having been anointed as Cohen Gadol in the first place, hence "asher yimshach oso," the accidental murderer is the cause for this person being appointed.
