Flight Instructor reported a left yaw during landing and stopped on the runway. Upon further inspection found the left tire deflated with no damage and was towed off runway.

Narrative

On final approach to Runway XX at ZZZ during a normal training mission to fly a traffic pattern with takeoffs and landings; the left main tire on the PA-28-181 became flat. Winds 050/17 Gusting to 26. Using Risk mitigation techniques; both commercial pilot (student) and Certified Flight Instructor agreed to fly as the conditions didn't exceed any aircraft limitation and both pilots are proficient with crosswind landings. On the initial touchdown; the impact was smooth with minimal load factor by way of proper crosswind landing techniques. Touchdown occurred approximately 50ft; beyond the aiming point markers on runway XX. Within 3-5 seconds (200 ft.) on ground roll the airplane suddenly experienced a yaw to the left. Directional control was maintained with the unknown condition at the time. Upon later findings; the left main tire was deflated and came to rest on the left side of runway centerline near the edge of the grass within 30 ft. feet of the 3000 ft. distance remaining sign. No injuries. Aircraft towed off of runway.