Someone once asked the question, If a person slew another person in a city of refuge, what would happen? Would they be forced to flee to another city of refuge? Using the text, there is a simple answer. The explanations of the town of refuge are in Numbers 35, Deut 4:41-43, and Deuteronomy 19.
The city of refuge is a safe place for someone who accidentally killed another person to hide from a relative of the victim who wants immediate vengeance. The slayer has to stay in a city of refuge until the presiding high priest dies. If they leave beforehand, they are not protected from an avenger. Initially, there were only six cities of refuge, three located east of the Jordan River and three west of it. The Israelites are allowed to add three more if their territory grows as a result of God’s blessings (Deut 19:8-9). Numbers 35:6 says that six of the cities that are set apart for the Levites should become cities of refuge. This means that these cities were unique, and Levites primarily lived in them. Furthermore, Numbers 35:25 states that the community was responsible for ensuring a person was safely escorted to a city of refuge, and Deuteronomy 19:3 specifies that these cities should be established in strategic locations that are easily accessible via roads.
The situation described would not have happened unless a Levite slays another Levite, or a refugee slays someone while in the city of refuge. The Levites are the tribe that works with the Tabernacle/Temple, and they aren’t even allowed to serve in the military, so I don’t think they can commit vengeance executions. That is why their cities are the cities of the refugee because it is supposed to be set apart as holy and free from violence. Based on what is written, if a Levite slays another Levite, they would just go straight to trial, and if it was not an accident, they could simply have them executed for murder. If it were an accident, since they are all Levites and are supposed to be more holy than the rest because they are directly attached to the priesthood, there would be an understanding that they cannot avenge the death. If a refugee who is already in the city for a slaying, accidentally kills a person within the city of refuge, I imagine that trial would happen only if he is found not guilty in the preceding trial for the accident that brought him to the city in the first place. If he is found not guilty in both trials, he lives and stays untouched until the high priest dies. I don’t believe the Levites can avenge their family members who were accidentally slain, since again, they are set apart as holy and didn’t even serve in the military.