Let's say: Go Shedinja! The opponent sent out Blissey! Shedinja used Final Gambit! How much damage would it do? It would be pretty hilarious if it was 1 Hp.
It would deal 1 HP, then Shedinja would faint.
Tested here.
Shedinja uses Final Gambit then faints and the damage on Blissey will be 1 HP. Source
Final Gambit does as much damage as the number of hit points the user has left. Since Shedinja can only hope to get 1 HP, that's all Final Gambit would do.
Hope I helped!