According to the flight instructor, during the turn from base to the final, the stall warning horn sounded and the aircraft descent rate increased. The flight instructor reported that he told the student pilot to go-around, and the student increased the power, but the airplane continued to descend and touched down on the runway briefly. He reported that the student then tried to "pull" the airplane off of the runway and either failed to apply sufficient right rudder, or accidentally applied left rudder, and the airplane abruptly yawed to the left. The flight instructor reported that he immediately took control of the airplane which exited the runway to the left. The flight instructor recounted that the airplane continued accelerating a few feet off of the ground. He reported that the airplane's left main landing gear struck the ground, and the "left wing tip must have scraped" the ground at that instant. He reported that he regained control of the airplane, initiated a climb, and executed a go-around. The flight instructor contacted the pilot of an airplane that was holding short of the runway and asked the pilot to look at the landing gear as he made a low pass. The pilot on the ground confirmed that the landing gear was intact. The flight instructor landed the airplane and contacted the operator. The airplane sustained substantial damage to the left aileron. The flight instructor reported that there were no mechanical failures or anomalies prior to or during the flight that would have prevented normal operation.