If Fiend Hunter leaves the battlefield before its first ability has resolved, its second ability will trigger and do nothing. Then its first ability will resolve and exile the target creature indefinitely. This is different from abilities on other cards that exile a permanent "until" something happens.

Once the exiled creature returns, it's considered a new object with no relation to the object that it was. Auras attached to the exiled creature will be put into their owners' graveyards. Equipment attached to the exiled creature will become unattached and remain on the battlefield. Any counters on the exiled creature will cease to exist.

If a token is exiled this way, it won't return to the battlefield.

In a multiplayer game, if you lose the game, the creature exiled with Fiend Hunter remains exiled indefinitely. This is also different from abilities on other cards that exile a permanent "until" something happens.