Alferd Packer - who keeps him?

While Alferd is in your posse, your opponent gains “Repeat Shootout, Pay 3 Ghost Rock: Alferd joins your posse, under your control.”

Situation: Player A owns, and has Alferd in a posse, and the opponent takes control of him. Player A doesn’t have the money to buy him back.
Question: Does Alferd go back to the owner at the end of the shootout, or does the opponent keep control of Alferd indefinitely (until the next shootout, when he may be taken back by the owner)?

Effects from Shootout plays end when the shootout ends.
Just like bullet modifiers wear off when a shootout ends, Alferd would convert back to the control of his owner when the shootout ends.