Boeing should be able to answer that one... it's a fly by wire aircraft, meaning you need power, both electrical and hydraulic to operate flight control surfaces. When the batteries and/or hydraulic accumulators deplete control is lost, however it seems to me that if I were designing the software I would have it monitor the power sources and assure that the aircraft was in best glide configuration prior to total loss of power. The 777 is supposedly a very stable aircraft, meaning if it were properly trimmed it may go on for some time with no control input, perhaps wallowing and porpoising a bit, but not doing what the movies and cartoons think planes do when they lose power... like zombies brought back to life that immediately need to strangle somebody, airplanes always stop in midair, pivot nose down and dive straight for the ground, usually to the sound of a Stuka dive bomber siren.
It's a good question. It's also why I hate being in any fly by wire aircraft not equipped with ejection seats.