The autopilot will hold all the way to stall warning, albeit with significant aileron roll input and some roll towards the dead engine. It will automatically disengage at stall warning, usually followed by a rapid roll towards the dead engine.
In my experience for the ones we deliberately don't brief first action, which is initiate a drift down aiming for 150kts, and at least point towards a suitable airport, so it's altitude select, just spin it down, IAS, rudder trim, then take action. For the ones that know everything and need a fright.
The unbriefed ones it goes something like this, flame out, eyes on engine instruments, look out the window to see if there's something to see, reach for the checklist, at which point the autopilot disengages followed by a snap roll toward the dead engine.
The end result, the prop was never feathered, the maximum speed was exceeded by around 40 kts at exercise termination. SIM ONLY of course.