I always drool when I sleep. I've found that it's only because I sleep on my stomach. When I sleep on my back, no drool.
I really can't sleep on my Back at all though. I find it so uncomfortable. Even when I was in the hospital with a broken foot, I filped over on my stomach and fell asleep (while waking in a puddle of drool).
I really don't like my drooling habit because whenever I wake up, if I want to go back to sleep, I have to lay down on a soaked pillow. Even turning the pillow around I can still feel wetness (due to drooling on the edge of my pillow too

).
As for sleeping deeply, my Mom said when I was sleep sometimes, I'd literally turn and fall out of the bed and remain sleep. o_O
Jam it back in, in the dark.