What happens if you bounce your own permanent in response to a spell that targets it?

When you 'bounce' a permanent — return it to your hand — in response to a spell that targets it, that permanent leaves the battlefield. Once it leaves, the spell's target no longer exists as a valid object on the battlefield. When the spell finally tries to resolve, the game checks whether its targets are still legal (CR 608.2b). If all targets are illegal, the spell is countered by the rules and has no effect.

This works because objects that change zones become entirely new game objects (CR 400.7). The permanent that went back to your hand is not the same object the spell was targeting, so the target is considered gone, not merely moved.

There is an important condition: this only fully saves you if the spell targets only that permanent. If the spell has multiple targets and at least one other target is still legal, the spell resolves but affects only its remaining legal targets (CR 608.2b).

Concrete example: Your opponent casts Pacifism targeting your Grizzly Bears. In response, you cast Unsummon on your own Grizzly Bears, returning it to your hand. When Pacifism tries to resolve, Grizzly Bears is no longer on the battlefield — its only target is illegal — so Pacifism is countered by the rules and goes to the graveyard with no effect. You can replay Grizzly Bears next turn, free of enchantments.

Note that 'hexproof' or 'protection' cannot be gained retroactively once a spell is already on the stack targeting you, but bouncing removes the object entirely, which is a different and complete solution (CR 115.5).