The helicopter flight instructor reported that, with he and the student both on the controls, about 10 feet above the ground, he initiated a simulated, engine failure autorotation with a power recovery. As they rolled the engine throttle up to recover, the alternator light came on and "the engine quit." About two feet above the ground, the flight instructor raised full collective, leveled the helicopter and the low rotor rpm light illuminated, and the horn sounded. The helicopter landed hard, bounced, settled back onto the runway, and the main rotor blade struck the tailboom. The pilot added that during the accident sequence, the alternator light turned off. The helicopter sustained substantial damage to the tailboom. The Federal Aviation Administration inspector reported that during his interview with the flight instructor, the pilot stated that the engine might have had a low idle setting and that during the accident flight, he applied full carb heat. The inspector added that due to the accident occurring more than 3 years before it was reported by an anonymous person, he was not able to determine the reason for a reported power loss. The instructor further reported that during a post-accident engine run, the engine started and ran without any issues.