Donpizmeof
If in the cruise and the fuel starvation point is reached, one engine could fail before the other. In this case, autothrust (autothrottle? been a while since I was on the Boeing) would command the live engine towards climb thrust (max cruise setting), and the autopilot would look after the rudder to keep things straight and try and maintain level. As the speed decays, slow speed protection will then cause the aircraft to descend. When the other engine fails, the engines may be rotating fast enough to keep the generators online (if the Tas is high enough), if not the RAT will deploy to keep electrics. Hydraulic pumps too will keep working as long as the engines rotate fast enough. Either way the autopilot and flight controls will remain active until ground impact.
I don't think it will be the dramatic departure from controlled flight that has been explained here previously.
Almost but not quite.
When the second engine fails the remaining generator and back up generator will drop off line and the autopilot will disconnect. The flight controls will then go into direct mode so you will lose a lot of the fancy stuff like bank angle protection and thrust asymmetry compensation.
The rudder trim that was added by TAC to compensate for being on one engine may or may not have stayed in depending upon how quickly the generator dropped off line. The Ram Air Turbine will deploy (although it takes a while to speed up) and then the autopilot can be reengaged. However if the pilots are incapacitated the autopilot will not reengage on its own and the flight controls will remain in direct mode. With unconscious pilots at the controls, autopilot disconnected and untrimmed since the second engine failure I would not expect the impact with water to be survivable.
However with empty tanks and a pilot flying it to a successful ditching, (much harder at night) I would have thought there was a fair chance of quite a few people surviving the impact. However the chances of getting into a slideraft and staying in it and detaching it in mountainous seas at night are probably not great.