After an uneventful touchdown for a full-stop landing, the pilot initially raised the nose of the airplane for the purpose of aerodynamic braking. She then lowered the nose wheel to the runway, and began to apply the wheel brakes. At that time she discovered that there was no resistance from the left brake pedal, and that the left brake was not working. Although she applied the right brake hard, that wheel began to skid, and the airplane departed the right side of the end of the runway. After departing the runway, the airplane's horizontal stabilizer impacted a runway sign support box. An inspection of the left brake master cylinder by a Federal Aviation Administration Airworthiness Inspector determined that it contained only residual hydraulic fluid near its bottom, and that fluid had been leaking past the shaft that protrudes from the master cylinder and connects to the brake pedal.