On September 19, 1997, about 1904 eastern daylight time, a Piper PA-28R-200, N4315X, registered to Grady and Francis, Inc., landed short of the runway while making a forced landing following loss of engine power at Kendall-Tamiami Executive Airport, Miami, Florida, while on a Title 14 CFR Part 91 personal flight. Visual meteorological conditions prevailed at the time and a visual flight rules flight plan was filed. The aircraft received substantial damage and the private-rated pilot and three passengers were not injured. The flight originated from Key West, Florida, the same day, about 1840. The pilot stated they were in cruise flight at 8,500 feet near Miami, Florida. He leaned the engine fuel mixture to 11 gallons per hour with the engine mixture control. The engine ran fine for a few minutes and then the fuel mixture began to lean further and the engine lost power. He placed the mixture control in the full rich position, but the mixture setting did not change. He placed all of the engine controls full forward with no response from the engine. With partial engine power he descended for a forced landing at Kendall-Tamiami Executive Airport. He had insufficient altitude and airspeed to make the runway and landed on soft terrain short of the runway. The landing gear collapsed during rollout and the aircraft skidded to a stop. Postcrash examination of the aircraft was performed by an FAA inspector. The mixture control cable hold down bracket, at the fuel control end of the cable, was found broken. Additionally a clamp attaching the mixture control cable to the engine mount was missing the rubber insert and the clamp moved freely on the engine mount arm. Movement of the mixture control caused the housing to move, but the inner cable would not move the mixture control arm on the fuel control. (See FAA Inspector Statement) The Piper Aircraft PA-28R Inspection Report requires that the security of the mixture control cable be inspected each 100 flight hours. (See attached Inspection Report)