The helicopter was damaged during an attempted simulated autorotation with power recovery. The flight instructor and the student pilot were on an instructional flight to practice straight and level, normal approaches and simulated forced landings. The instructor reported that the student completed two successful approaches and one successful autorotation with power recovery. The instructor stated that on the last autorotation the student maintained speed and initiated the flare and held it until the instructor felt the aircraft was too low to hold. The instructor reported taking the controls and pushing the cyclic forward at the same time as the student pilot began to push forward. The instructor reported feeling the impact of the tail rotor and boom, then the aircraft yawed to the right. The instructor stated that the throttle was already closed to idle so the instructor "held the cyclic for a level attitude and prepared to cushion the landing with the collective. [The helicopter] spun around approximately another 390 degrees to the right before the helicopter impacted the runway on the skids collapsing the left side of the landing gear."