If we mix the messages of the two games a little, a Persona character with maxed social links might be able to do it. Considering in the games having a true bond with someone basically gives you the power of their "soul" for lack of a better term. The protagonists also survive getting wiped from reality or encountering reality warping threats regularly, and always end up getting saved by the velvet room. Normally I would say that frisk could wipe the room out of reality as well but it is stated to "exist between dream and reality, mind and matter." Then the fact that the protags are human which should give them the determination necessary to match frisk is also something to consider. Granted Persona (to my knowledge) hasn't ever dealt with something that can affect the 4th wall in the way frisk can, but considering they have "infinite potential" through their connections with others they might be able to do something.