If Quicksmith Rebel leaves the battlefield, you no longer control it.

If another player gains control of Quicksmith Rebel, the artifact will no longer have the damage-dealing ability, even if you regain control of Quicksmith Rebel.

If Quicksmith Rebel leaves the battlefield while its ability is on the stack, the artifact never gains the damage-dealing ability.

If Quicksmith Rebel or the artifact leaves the battlefield while the damage-dealing ability is on the stack, that ability resolves as normal.