In a multiplayer game, if the owner of In the Trenches leaves the game, the exiled card will return to the battlefield. 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.

The activated ability can only be activated once per game. If the ability is countered or otherwise fails to resolve after being activated, it can't be activated again.

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

If In the Trenches leaves the battlefield and later returns to the battlefield, it is a new object on the battlefield with no memory of the last time it was there. Its ability may be activated, even if it was activated a previous time it was on the battlefield.

If In the Trenches leaves the battlefield before its activated ability resolves, the target permanent won't be exiled.

The activated ability is a single ability that creates two one-shot effects: one that exiles the permanent when the ability resolves, and another that returns the exiled card to the battlefield immediately after In the Trenches leaves the battlefield.

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