Slippery Pete
If this is simply as it appears... Autofeather #2 (perhaps ATPCS error, doesn't matter) followed by crew pulling torque off and eventually shutting down the operating engine, then the lesson to be learnt is very simple.
Why the #### are these things being shutdown close to the ground? At one turboprop operator I worked for, they were adamant the shutdown with a V1 failure was to be done at acceleration - sometimes as low as 500'. It was mind bogglingly stupid, but it still happens in turboprop sims the world over.
The only reason a shutdown should be actioned so low is for engine failure followed by failure to auto feather (a desperate situation indeed, yet one which had NEVER occurred since type certificate issue, worldwide, on the airframe I used to fly).
The case of a fire may also warrant an immediate shutdown, but should be with fire handle and fire handle alone.
Manipulating power levers and fuel shutoffs just after takeoff when one propeller has auto feathered and the aircraft is still completely climb-able and controllable is just nuts.
That's why these damn things have auto feather in the first place.
If it's climbing, sit on your hands and keep it flying. Anything and everything else can wait.
I hope desperately this was not a case of shutting down the only engine which was developing power.]
Agree ...... but
I'm still open minded that the aircraft having lost the thrust from one engine may have been continuing to lose flying performance from as yet the unexplained symptoms from the remaining engine. The crew may have reason to believe that they could only regain the full power on the remaining engine by restarting it.
This is only speculation on my part but surely it should be vetted in the onward investigation