THE NEW OWNER OF THE ACFT WAS RECEIVING FLT TRAINING FROM AN INSTRUCTOR (CFI) & THEY WERE PRACTICING LANDINGS. DRG A LANDING ROLL-OUT, THE ACFT BEGAN TO VEER TO THE RIGHT. THE CFI TOOK THE CONTROLS TO AVOID RUNNING OFF THE RWY, THEN TOOK OFF & FLEW ANOTHER PATTERN. ON FINAL APCH, THE STUDENT TOOK THE CONTROLS AGAIN TO MAKE THE NEXT LANDING. DURING THE ROLL-OUT, THE AIRPLANE AGAIN STARTED A SHARP RIGHT TURN. THE CFI RPRTD THAT FULL LEFT RUDDER & BRAKE DID NOT STOP THE TURN & THE ACFT DEPARTED THE RUNWAY TO THE RIGHT. THE LEFT MAIN GEAR COLLAPSED AS THE ACFT WENT OFF THE RWY. ALSO, THE LEFT WING, ELEVATOR, FUSELAGE & CABIN AREA WERE DAMAGED. THE CFI NOTED THAT THE OWNER WAS OF SMALL STATURE & THE SEAT HEIGHT WAS NOT ADJUSTABLE. THE CFI HAD WARNED THE OWNER THAT THE 'CLEVELAND BRAKES' WERE VERY POWERFUL & EFFICIENT.HE BELIEVED THE OWNER MAY HAVE INADVERTENTLY APPLIED RGT BRAKE WHILE APPLYING LEFT RUDDER.