Can (does) one who has murdered and must go to a refuge city own property there?
Specifically real estate, this would make a difference regarding his obligation to come to the temple three times a year. Although he is exempt from doing any Mitzvah which would require him to taking leave of the city, according to the Talmud (Rebbi Ami, Pesachim 8b) if one does not have property he is exempt from the pilgrimage.
I can see two sides to this. Perhaps this is another reason he is exempt, since he cannot own land, or perhaps he is required to appoint a proxy of sorts (and then this is also a broader question of appointing a proxy for other obligations he cannot leave for per Mishnah Makos 2:7 and Rozteach 7:8 but - why shouldn’t he be able to do good from behind bars, if he can?).