The certified flight instructor (CFI) and a student pilot, who held a foreign-issued fixed-wing certificate, were on a local training flight. The purpose, in part, was to practice autorotations. The CFI demonstrated the first autorotation. The CFI entered the autorotation after saying "…entering autorotation in 3-2-1" and lowered the collective while simultaneously adding right pedal for trim. Once the collective was all the way down, she closed the throttle. The CFI began to recover at an altitude of approximately 1,000 feet by cracking open the throttle and letting the governor take over after 80 percent revolutions per minute (RPM). Prior to letting the student take the controls, she reviewed the recovery procedure again. The CFI remained on the controls while the student did the control applications. One autorotation was performed successfully. The student entered his second autorotation and at 1,000 feet above ground level, the CFI requested that the student perform a recovery. The student rolled on the throttle and the CFI felt a yaw to the right. The CFI countered with left pedal and stated "I have the controls" and the student relinquished all controls. The CFI noted that the engine and rotor RPMs were excessively high so she decreased the throttle to lower the engine RPMs. She began to raise the collective to lower the rotor RPM, but neither of the RPM needles decreased. The helicopter was maintaining a level attitude but got closer to the ground. As they neared the ground, she looked for a place to land. During the landing, the low rotor RPM horn sounded and the helicopter touched down on the ground. They exited the helicopter and saw that the tail boom had separated. The CFI reported no preimpact mechanical malfunctions or failures with the helicopter that would have precluded normal operation.