There are many important moments in the story, but the most crucial—called "story spotlights"—are shown on cards. These cards have the Planeswalker symbol in their text box; this symbol has no effect on gameplay. You can read more about these events in the official Magic fiction at http://www.mtgstory.com.
In a multiplayer game, if Ixalan's Binding's owner leaves the game and another player owns the exiled 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 the exiled card has a different name in exile than it did on the battlefield, Ixalan's Binding stops players from casting spells with the name of that card as it exists in exile.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Chase Stone
Card data via Scryfall. Rarix is fan-made; not endorsed by the rights holders.
If there is no exiled card (perhaps because the exiled permanent was a token or was a commander that was moved to the command zone in a Commander game), Ixalan's Binding won't stop players from casting spells.
If the exiled card is a land card that's become a nonland permanent, Ixalan's Binding won't stop players from playing lands with that name.
If Ixalan's Binding leaves the battlefield before its triggered ability resolves, the target permanent won't be exiled.
Auras attached to the exiled permanent will be put into their owners' graveyards. Any Equipment will become unattached and remain on the battlefield. Any counters on the exiled permanent will cease to exist.
If a token is exiled this way, it will cease to exist and won't return to the battlefield.
The exiled card returns to the battlefield immediately after Ixalan's Binding leaves the battlefield. Nothing happens between the two events, including state-based actions.
