I wonder what the rules are in such a case: is the tournament director allowed to intervene, or does the game end abruptly when the player who fell asleep as it was his turn to move oversteps the time limit? Would that mean the other player won the game while sleeping?
In theory, it is not legal to "disturb" a player, and waking one up is surely disturbing him. On the other hand if the player snores he is disturbing others, in which case it is theoretically legal for the tournament director to wake him up. So apparently if one does fall asleep during a game, one should hope one snores, since otherwise one would lose on time.