During the time of Redemption, the laws of the "Cities of Refuge" will go back into effect--someone who kills by accident will need to run to one of these cities to escape revenge by the goel hadom, the relative of the deceased who serves as the "blood avenger."

However, if during the time of Redemption we will all live everlasting life, then surely there will be no killing, deliberate or accidental. What, then, will be the purpose of these cities of refuge? The Shach, in his commentary on the Torah, explains that the purpose of the cities of refuge is to serve as an atonement. One who is exiled to a city of refuge moves there with his family and even his teacher, since exile is a process of spiritual development. This holds true even if there is no "blood avenger" who is after him.

 The cities of refuge will serve not for new killers, but for all those who are resurrected who were responsible for causing accidental death. During all the years of exile, they were not able to complete their atonement, since the cities of refuge were not in effect. The Torah even commands that three new cities will be added, in territories that will be joined to Israel after the Redemption. The cities will be situated conveniently so that anyone who is in need of this form of atonement will be able to easily reach them.

Likutei Sichos vol. 24, p. 111. Toras Menachem, 5746, vol. 4, p. 351