The certificated flight instructor (CFI) stated that during a local training flight he was demonstrating how to perform a run-on landing to the student pilot. During the landing, the helicopter began to travel toward the right edge of the paved surface. The CFI stated he countered the right slide with left cyclic input. As the helicopter approached the paved surface edge, the CFI raised collective in order to attempt put the helicopter into a hover but the helicopter left the paved surface. The helicopter subsequently rolled over on to the right side, which resulted in substantial damage to the tail boom, main rotor blades, and fuselage. According to a written report, there were no mechanical malfunctions with the helicopter prior to the accident.