The flight instructor reported that, while landing at night, the pilot receiving instruction allowed the twin-engine airplane to drift left of the centerline at touchdown. The pilot then overcorrected with right rudder, the airplane veered to the right, and the pilot then locked the brakes. The airplane continued to veer right and exited the runway. The flight instructor added that he did not ask for the flight controls but that he did ask the pilot to release the brakes; however, the pilot did not do so. After exiting the runway, the flight instructor had only right rudder and nosewheel steering and "fishtailed" the airplane further to the right before the left main landing gear collapsed. The airplane sustained substantial damage to the left wing. The flight instructor reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation. The automated weather observation system on the airport reported that, about the time of the accident, the wind was from 230° at 9 knots. The pilot landed the airplane on runway 21.