On December 17, 2013, about 1130 central standard time, a Cessna 305C (0-1E) airplane, N83CN, was substantially damaged during a runway excursion and ground loop after an aborted landing attempt at the South Texas Regional Airport (HDO), Hondo, Texas. The private pilot was not injured and the flight instructor sustained minor injuries. The aircraft was registered to and operated by the private pilot under the provisions of 14 Code of Federal Regulations Part 91 as an instructional flight. Visual meteorological conditions prevailed for the flight, which was not operated on a flight plan. The local flight originated from HDO about 1100.The flight instructor reported that he and the private pilot were conducting a flight review at the time of the accident. After completing some airwork, they returned to the departure airport to complete some takeoffs and landings. He noted that the first two landings resulted in a left turning tendency during the landing roll on the hard surface runway. For that reason, the instructor decided to complete the next landing, which he did as a three-point landing with "minimal directional control problems." The next landing was completed by the private pilot, which continued with a left turning tendency and resulted in an aborted landing. The final landing also resulted in an attempted aborted landing; however, a "severe left turn" developed resulting in a runway excursion, ground loop and landing gear collapse. The instructor added that the flight should have been terminated in order to investigate the left turning tendency. The airplane came to rest upright on the grass/dirt infield area adjacent to the runway. The outboard one-third of the right wing was deformed upward. The landing gear had collapsed. A postaccident examination of the landing gear did not reveal any anomalies consistent with a preimpact failure. However, the left main landing gear attachment bolt was not recovered, which precluded a complete examination of the landing gear assembly. The observed wind about the time of the accident ranged from variable to westerly at 4 to 5 knots. The pilot reported a southerly wind at 4 to 5 knots, with no gusts and no turbulence.