Robert,
The 777 is FBW. It does not require trimming for power changes, only for speed changes. Once its trimmed, and autothrottles are looking after the speed its very stable, and flies very nicely hands free.
There are plenty of incidents where aircraft have continued on autopilot after the crew have become incapacitated.
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.