AN MU300 FLT HAS A BRAKE FAILURE ON ROLLOUT AND ENDS UP 15 FT INTO THE OVERRUN OFF RWY 14 AT APF; FL.

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LNDG AT NAPLES; FL (APF); THE ACFT HAD A BRAKE FAILURE AND CAME TO STOP IN THE OVERRUN APPROX 15 FT. DAY; VMC CONDITIONS; FLT ORIGINATED AT FLL. CLRED FOR A VISUAL APCH AT APF. LNDG WT 12700 LBS. USED A VREF OF 108 WHICH IS COMPUTED FOR 13000 LBS. HELD AN APCH SPD OF 120 KTS ON FINAL UNTIL OVER THE APCH END OF RWY 14. TOUCHED DOWN APPROX 800 FT PAST APCH END; LEAVING 4200 FT TO BRING ACFT TO A STOP. COMPUTED STOPPING DISTANCE WAS 2800 FT. TOUCHED DOWN AT VREF (108) CALLED FO TO APPLY SPD BRAKES; MADE A GOOD BRAKES CALL. INITIALLY ACFT MADE A HARD DECELERATION; SO I EASED UP ON THE BRAKE PRESSURE IN ORDER TO CARRY SOME FORWARD MOTION TO EXIT OFF THE RWY AT THE VERY END. REAPPLIED BRAKE PRESSURE AT APPROX HALF WAY POINT AND BRAKES FAILED. ACFT LEFT RWY AND CAME TO STOP 15 FT IN OVERRUN. NO ACFT DAMAGE; NO INJURIES TO PAX. INSPECTION OF RWY REVEALED R BRAKE LOCKED UP WITH SKID MARK; AND NO L BRAKE SKID MARK. ANTI-SKID WAS ON; AND TESTED OK PRIOR TO FLT. SUPPLEMENTAL INFO FROM ACN 587269: BRAKE PRESSURE WAS RELEASED TO ROLL TO END OF RWY 14 TO MAKE A L TURN OFF AT THE END OF RWY 14 -- PIC WENT TO APPLY BRAKES TO NEARLY STOP ACFT TO MAKE 90 DEG TURN OFF OF RWY 14 AND HAD NO BRAKES. AS THE SIC; I PLACED MY FEET ON BRAKES AFTER HE ANNOUNCED TO TWR THAT WE HAD A BRAKE FAILURE AND THERE WAS NO BRAKE PRESSURE AT ALL. AT THIS TIME AIRSPD INDICATOR IS NOT REGISTERING. WE WERE TRAVELING APPROX 8-10 KTS; NOT VERY FAST AT ALL BUT TOO FAST TO MAKE A 90 DEG TURN TO THE L TO EXIT THE RWY ONTO TXWY.