The flight instructor and pilot receiving instruction were landing a tailwheel-equipped airplane. The instructor reported that that the after touchdown the airplane veered to the right. He took control of the airplane and applied full left rudder and left brake. The airplane tracked straight for a moment before it turned right and departed the runway. The left main landing gear collapsed and the left wing impacted the ground. Examination of the airplane's right brake rotor revealed heat damage (bluing) of the rotor and substantial damage to the airplane's wing and fuselage. The instructed noted that the other pilot did not appear to make any control inputs that would have resulted in a right turn.