For Pokémon with 1 HP, leftovers would never heal them. Because their HP is either full, or they are fainted. And leftovers doesn't heal in any of these instances.
So for Pokémon with HP ranging from 2 - 15, the amount of HP regained would be rounded up to 1. They wouldn't not be healed, because the leftovers always heal (apart from in the mentioned instances). And their HP wouldn't be restored by a fraction, because, that just doesn't happen! So their HP would be restored by 1 each turn, as if it had 16 HP.
Source: Knowledge and Experience
I hope I helped!