Hostage Taker

In a multiplayer game, if a player leaves the game, all cards that player owns leave as well. If you leave the game, any spell or permanent cards you control from Hostage Taker's ability are exiled.

In a multiplayer game, if Hostage Taker's owner leaves the game while the card is still exiled and another player owns that card, the exiled card will return to the battlefield under its owner's control. Because the one-shot effect that returns the card isn't an ability that goes on the stack, it won't cease to exist along with the leaving player's spells and abilities on the stack.

If it's still in exile, the exiled card returns to the battlefield immediately after Hostage Taker leaves the battlefield. Nothing happens between the two events, including state-based actions.