Briefly:
Jacob Milgrom in
The JPS Torah Commentary: Numbers notes regarding Numbers 35:25 ...
As the High Priest atones for Israel's sis through his cultic service in his lifetime (Exod. 28:36; Lev. 16:16,21), so he atones for homicide through his death. Since the blood of the slain, although spilled accidentally, cannot be avenged through the death of the slayer, it is ransomed through the death of the High Priest, which releases all homicides from their cities of refuge.That it is not the exile of the manslayer but the death of the High Priest that expiates his crime is confirmed by the Mishnah: "If, after the slayer has been sentenced as an accidental homicide, the High Priest dies, he need not go into exile." The Talmud, in turn, comments thereon: "But is it not the the exile that expiates? It is not the exile that expiates, but the death of the High Priest." [pg. 294]
Milgrom then refers the reader to Excursus 76 that more fully addresses the biblical concept of bloodguilt, the consequent pollution of the land, and the expiation required.