Terisian Mindbreaker

If you activate a card's unearth ability but that card is removed from your graveyard before the ability resolves, that unearth ability will do nothing as it resolves.

At the beginning of the next end step, a permanent returned to the battlefield with unearth is exiled. This is a delayed triggered ability, and it can be countered by effects such as Defabricate that counter triggered abilities. If the ability is countered, the permanent will stay on the battlefield and the delayed triggered ability won't trigger again. However, the replacement effect will still exile the permanent if it eventually leaves the battlefield.

Unearth grants haste to the permanent that's returned to the battlefield (even if it's not a creature card). However, neither of the "exile" abilities is granted to that permanent. If that permanent loses all its abilities, it will still be exiled at the beginning of the next end step, and if it would leave the battlefield, it is still exiled instead.