Before the Israelites had even entered the promised land, God had given them a plan, expecting them to care for the Levites and give them forty-eight cities and suburbs. Six were to be cities of refuge where accidental murderers could escape until the due process of the law or until the high priest died. They could stay in the city of refuge, safe from the avenger, but if they left and the avenger saw them outside of the city's boundaries, they were at risk of being killed. They couldn't go home. However, they could return to their land once the high priest died. The scripture doesn't give any detail as to why, so my thoughts are that when the priest died, he carried the murderer's guilt with him. I'm not sure if that's true, but if you look at what Jesus did by dying on the cross for us, it's similar; he took on the guilt of our sin, freeing us from the consequences. Jesus is our city of refuge; we must stay within his boundaries. If we venture outside his gates, we risk receiving compensation for our sins. I'll bet that living among the Levites taught the murderers a lot about what God expected of them and probably helped comfort them for their guilty conscience. Learn from Jesus while seeking refuge, follow his teachings, love God, and love people, and it will be easy to stay in His city until the day he calls us home or returns.
Then ye shall appoint you cities to be cities of refuge for you; that the slayer may flee thither, which killeth any person at unawares. Numbers 35:11