The flight instructor and pilot-receiving-instruction reported that upon landing, the airplane immediately veered left followed by a noticeable vibration. The flight instructor attempted to correct with opposite rudder, however, the left veer continued, and the airplane struck a runway edge light which collapsed the left main landing gear. The airplane departed the runway surface and came to rest upright in the grass. The airplane sustained substantial damage to the left wing. Postaccident examination found that the left tire had excessive wear and a flat spot in the casing with a corresponding 2” hole. Additionally, ground scars observed prior to the runway edge light showed that the tire casing had separated from the tire rim. It is likely the tire was in a near flat condition during the landing which resulted in the loss of directional control.