but the speed would start to bleed off due to the thrust reduction and control inputs. As the speed bleeds off the A/P will try to hold the altitude and then eventually disconnect.
Not on the 777 I flew. If the TAC can handle the asymmetry,
(debatable without a bit of help from a friendly foot - the TAC is not designed to do all the work, just to assist, and it gives different percentages of assistance in cruise than on takeoff), once the speed reduces to the lower envelope protection, the aircraft will descend, maintaining that min safe speed, I think at 300fpm, a more than acceptable rate of descent for a ditching.