When this enchantment enters, exile target creature an opponent controls until this enchantment leaves the battlefield. You gain 2 life.
If Makeshift Binding leaves the battlefield before its triggered ability resolves, the target creature won't be exiled, but you'll still gain 2 life.
If the target creature is an illegal target as Makeshift Binding's ability tries to resolve, it won't resolve and none of its effects will happen. You won't gain life.