Flight Instructor reported normal brake system failed on landing; resulting in a runway excursion and damage to the aircraft.

Narrative

IFR Flight from ZZZ1 to ZZZ. Brakes checked good visually and physically before departure. Landing at ZZZ went smoothly; however upon rollout and attempt to slow for left-hand taxiway; discovered left brake had lost all pressure and right brake had low pressure. Advised Tower of losing brake pressure; and was offered any necessary assistance. Continued ground roll with as much influence as pedals would allow. Eventual slowdown and residual brake pressure on right side began causing a mild turn to the right. Aircraft slowed to point of virtually no directional control and rolled off right edge of runway at approximately 2-3 MPH and 5-6 ft. off runway where grass stopped remaining momentum. Made sure to hold controls back to keep nose higher off ground to avoid prop damage and shut down systems when plane started to slip off runway. Alerted Tower we had lost all brakes and were stranded partially on runway. No visual damage to either aircraft or runway environment. Tower sent assistance with tow to FBO and called to confirm we were safe. Local mechanic confirmed a rubberized brake line rupture underneath pedals likely due to rubbing against edge of sheet metal concealed under floor plate.