I suppose the "passengers are asleep" comment implies that it's an overnight flight, which is why it would be relevant. Is that correct, AT463?
Like AIRWAY said, pilots work in shifts on long-haul flights. Those flights are manned with an extra pilot (or pilots, depending on the length of flight). During the course of the flight, the pilots will each rotate through a crew-rest break (e.g., one--or two, if there are two extra pilots--will sleep, while the others will fly*).
*Different companies may do the exact rotation/break schedule differently, but in all cases the cockpit is fully manned with the required number of pilots at all times.
And no, pilots never just leave the whole operation of the aircraft to the autopilot--perhaps that's just something people see in movies, but in reality it would be foolish. An autopilot is a tool which helps us maintain a desired flight path, but it can't think, assess upcoming weather and/or other hazardous situations, or make decisions.
Hope this helps with your questions.