Someone could flee there who committed manslaughter, killing his neighbor accidentally without previously hating him. He could flee to one of these cities and stay alive:

Then I fell down like the first time in the presence of the Lord for 40 days and 40 nights; I did not eat bread or drink water because of all the sin you committed, doing what was evil in the Lord’s sight and provoking Him to anger.

Otherwise, the avenger of blood in the heat of his anger might pursue the one who committed manslaughter, overtake him because the distance is great, and strike him dead. Yet he did not deserve to die, since he did not previously hate his neighbor.

they will bring the woman to the door of her father’s house, and the men of her city will stone her to death. For she has committed an outrage in Israel by being promiscuous in her father’s house. You must purge the evil from you.