On July 21, 1998, at 1500 central daylight time, a Cessna 150M, N9251U, piloted by a student pilot, received substantial damage on impact with a pole following a forced landing on runway 09 (3901' x 75', asphalt/dry) at Litchfield Municipal Airport, near Litchfield, Illinois. Visual meteorological conditions prevailed at the time of the accident. The personal 14 CFR Part 91 student-solo cross-country flight was operating on a flight plan. The pilot reported no injuries. The flight departed Greater Peoria Regional Airport, near Peoria, Illinois, at 1345 and was returning to St. Louis Regional Airport near Alton, Illinois. The pilot reported that the engine began to vibrate and run very rough at approximately 1445, near Carlinsville, Illinois, at an altitude of 4500' MSL. He noticed an immediate loss of power and was unable to maintain altitude. The pilot then cycled the magnetos, increased the mixture control to full rich, confirmed that the fuel selector was in the "ON" position and applied carburetor heat, all of which had no effect. Being uncertain as to the cause of the power loss and concerned that the engine would quit operating, the pilot declared a mayday and requested vectors to Litchfield Municipal. At the time the pilot made visual contact with the airport, the aircraft was at an altitude of 1100' MSL. The pilot chose to land on runway 09 even though there would be a quartering tailwind present upon landing. During the landing rollout, the pilot felt the tail swing to the left at which time the airplane departed the runway towards right into the grass, impacted a concrete culvert, separated the right main wheel and slid to a stop. The pilot stated that landing was made with full flaps. Examination of the engine by a Federal Aviation Administration Maintenance Inspector revealed that the number three cylinder had a compression of 35/80 and the number four exhaust valve was stuck in the full open position. The Pilot's Operating Handbook for a Cessna 150M states that the maximum demonstrated crosswind velocity is 12 knots. A Wind Components graph containing wind component, headwind or tailwind, versus crosswind component is also included.