My experience is a carb cleaning is usually necessary after running out of fuel. A quick test wouldn't hurt. Unplug the PTO at the connector closest to the PTO and then try and turn on the PTO and see if the engine still stalls. If it stalls you know that it's a issue in the safety system, if...
This style stator brake was most likely rushed out to meet new safety standards, stopping the blades faster when the safety switches cut the engine. The OP is now finding out why newer version of this have their own winding on the stator for the brake. I'm betting the relay failed while he was...
Here is a schematic that includes a startor brake. The model number you listed doesn't seem to include one in it's schematic, maybe there was an engine or wiring harness swap in its past.
It's probably a stater brake designed stop the engine quicker when powered off. They were fairly common on these kohler equipped craftsmans of this era.