This would be cause for immediate termination. I don't think there are any domestic flights that allow for crew rest.
As I generally sit in 1C I've seen this happen a number of times. I normally go to the galley and chat with them for a few minutes if it looks like they're ready to fall asleep.
There's an FA that flies out of one of the smaller bases for DL that is a known narcoleptic. Everybody at her base knows about it and all the other FA's watch out for her.....seen her pass out a number of times on the jump seat and used to think it was funny before I knew that she could lose her job over this.