800.4a. When a player leaves the game, all objects (see rule 109) owned by that player leave the game, any effects which give that player control of any objects or players end, and all spells and abilities controlled by that player on the stack cease to exist. Then, if there are any objects still controlled by that player, those objects are exiled. This is not a state-based action. It happens as soon as the player leaves the game. If the player who left the game had priority at the time he or she left, priority passes to the next player in turn order who’s still in the game.
I thought the permanent would be exiled, but there is a ruling on Agent of Treachery that states
Agent of Treachery’s effect lasts indefinitely. It doesn’t wear off during the cleanup step, and it doesn’t expire if Agent of Treachery leaves the battlefield. In a multiplayer game, it does expire if you leave the game.
Which I assume means that the controlled permanent goes back to Bob. However, looking at a similar card Beguiler of Wills, which also takes control of a permanent (creature), there are no special rules that state "In a multiplayer game, it does expire if you leave the game.". Which means that the controlled creature will be exiled when Alice leaves the game (according to ruling 800.4a if I am not mistaken).
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