SR20 student pilot reported losing directional control after landing; resulting in runway excursion. Post flight maintenance inspection showed that a brake pad was missing from the left brake assembly.

Narrative

Solo Cross-Country - Brake Failure Incident at ZZZDuring the completion of my solo cross-country flight; I encountered a full left brake failure upon landing at ZZZ. The aircraft and initial taxi were normal. However; as I reached Taxiway 1 at ZZZ1; I noticed an unusual squeaking sound coming from the left brake. In my past experiences; I had heard abnormal brake noises and did not initially consider this sound to be of significant concern.I tested the brake pressure on Taxiway 1 2-3 times; and the brake pressure appeared normal. I maintained consistent brake pressure for the remainder of my taxi and during the engine run-up. Based on this; I decided to continue with the flight.During the landing rollout at ZZZ; approximately 1;000 feet down the runway; I noticed the aircraft yawing to the right. I attempted to correct this by applying left brake and rudder. However; I quickly noticed the left brake pressure deteriorating. I then applied full left rudder and aerodynamic braking in an attempt to maintain the centerline and slow the aircraft.As the aircraft continued to yaw right toward Taxiway 2; I struggled to maintain directional control. With little to no left brake pressure; the right main landing gear went off the runway and into the grass. Fortunately; it quickly returned to the taxiway. I communicated with the Tower; informing them of the brake failure and requesting permission to stop the aircraft. After receiving clearance; I applied the parking brake and brought the aircraft to a complete stop.I then followed the engine shutdown checklist and exited the aircraft. After departing; I immediately contacted my flight instructor to report the situation. He promptly arrived at ZZZ with an AMT.Upon inspection; the AMT discovered that the left brake pad was missing. The brake pad was later found on Taxiway 3 at ZZZ1.