"And I suppose, if it's one last chance to say it, Rose Tyler..."

Grasp of Fate

When this enchantment enters, for each opponent, exile up to one target nonland permanent that player controls until this enchantment leaves the battlefield. (Those permanents return under their owners' control.)

Doctor Who

"The witch wrapped her heart in briar vines, hid it away in the ancient keep in the depths of the forest. If none could find it, the prophecy could never come to pass."
—*Beyond the Great Henge*

Wilds of Eldraine: Enchanting Tales

When Grasp of Fate enters the battlefield, for each opponent, exile up to one target nonland permanent that player controls until Grasp of Fate leaves the battlefield.

Auras attached to exiled nonland permanents will be put into their owners' graveyards. Equipment attached to exiled creatures will become unattached and remain on the battlefield. Any counters on exiled nonland permanents will cease to exist.

If Grasp of Fate leaves the battlefield before its triggered ability resolves, no nonland permanents will be exiled.

If a token is exiled, it ceases to exist. It won't be returned to the battlefield.

In a multiplayer game, if Grasp of Fate's owner leaves the game, the exiled cards will return to the battlefield. Because the one-shot effect that returns the cards 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.

The exiled cards return to the battlefield immediately after Grasp of Fate leaves the battlefield. Nothing happens between the two events, including state-based actions.