Flight Instructor on training flight with student reported brake failure on landing rollout. Aircraft departed the runway and rolled to a stop in the grass.

Narrative

I was the CFI training a student in a Cirrus SR22 single engine aircraft. The weather was clear skies and calm winds. The preflight inspection was completed with nothing abnormal noted. The run-up was completed and nothing abnormal was noted. We departed ZZZ1 and the student performed the takeoff. We took a short flight to ZZZ for takeoff and landing training. We entered the pattern at a 45 degree angle for the left downwind of Runway XX. The student performed 4 full stop landings with taxi back via Taxiway 1 to Runway XX without any issues. On the 5th landing the student touched down about 50-100 feet past the landing markers and on speed; well within the first 3rd of the 5;003 feet runway; and immediately had trouble slowing down the airplane. I took positive control of the airplane and the right brake was completely inoperative. The left brake was fully functional. The throttle was completely closed and I kept the airplane on the centerline as long as I could using the left brake and right rudder only. Once speed decreased more the right rudder input became completely inoperative and I was forced to decrease braking pressure on the left pedal to remain straight on the runway. Once we were past the last 3rd of the runway it was clear we did not decrease enough speed to successfully stop on the runway. I continued to use left brake and right rudder; but the plane veered off the left side of the runway. We finally came to a stop in the grass about 30-40 feet on the left side of the runway. We were able to push the airplane to the ramp. Once the aircraft was on the ramp I got back in to check the brakes and the left pedal was still operative (could feel resistance) and the right pedal went straight to the floor without any resistance. The student alerted me the brakes were inoperative immediately and we were able to successfully stop the aircraft without any damage. The Cirrus SR22's free castering nose wheel uses differential braking to steer; so it was very difficult to steer without operating brakes on one side.