The flight instructor and the pilot-receiving-instruction were conducting a nighttime currency/proficiency flight when, after an uneventful landing flare and touchdown, the airplane began to vibrate and veer right during the landing roll. The pilot-receiving-instruction, who was the pilot flying during the landing, released toe brake input but the vibration increased as the airplane continued to veer right. Ultimately, the right main landing gear collapsed, and the airplane came to rest upright in the grass adjacent to the runway. The right wing main spar was substantially damaged when the right wing struck the ground after the landing gear collapsed. Examination of the right main landing gear tire and its tube revealed a sidewall puncture. The puncture was made by an unknown small, sharp object, which left a clean cut on the tube sidewall that measured about 0.25-inch long with the tube deflated, and 0.375-inch long when the tube was reinflated. During the landing roll, it is likely that the tube lost enough pressure that it began to move around the wheel rim until the valve stem severed and there was total loss of remaining tire pressure. The increasing vibration felt by the pilots during landing roll is consistent with a progressive loss of tire pressure, and the increased drag from the deflated right tire would explain airplane’s tendency to veer right. The right main landing gear likely collapsed when the over-center down lock assembly disengaged due to an excessive sideload during the right swerve.