THE CERTIFICATED PRIVATE PILOT WAS RECEIVING AN AIRPLANE MAKE AND MODEL COMPANY CHECK-OUT FROM A CERTIFIED FLIGHT INSTRUCTOR (CFI). WHILE EXECUTING A NO FLAP APPROACH THE CFI FAILED TO ADEQUATELY SUPERVISE THE FLIGHT BY FAILING TO MONITOR THE AIRSPEED. THE PRIVATE PILOT FAILED TO MAINTAIN THE AIRSPEED TO THE POINT THAT THE AIRPLANE STALLED AND LANDED HARD. AFTER LANDING THE AIRPLANE PIVOTED TO THE LEFT AND CONTINUED DOWN THE RUNWAY UNTIL THE MAIN AND NOSE LANDING GEARS COLLAPSED FROM OVERLOAD.