As for the 777 A/T wake-up function, if you descend with 'speed on elevator', the most common mode being FLCH (God's version of V/S) and then do not quite capture the Altitude, i.e. disregard the last few seconds of the flight director commands during the ALT CAP phase, the aircraft will sit there, in level flight with the F/D commanding 'fly down', the pilot disregarding the commanded manoeuvre and the speed decreasing to the stall with NO response from the A/T.
We established that during the certification programme in the early/mid 90's.
Try it next time you are in the simulator.