On January 21, 1997, at 1732 eastern standard time (est), a Beech 300, N404EW, registered to E W Marine of Elkhart, Indiana, and operated by a Airline Transport pilot, ran off the end of runway 35 (6500' x 150' wet/asphalt) after experiencing a tailwind on touchdown at Monroe Country Airport, Bloomington, Indiana. The airplane sustained substantial damage when its landing gear collapsed. The pilot and ten passengers reported no injuries. The personal 14 CFR Part 91 flight was operating in instrument meteorological conditions. An IFR flight plan was filed. The airport weather at the time of the accident was reported as 1/8 mile in fog with a variable ceiling of 200 feet. The flight departed Elkhart, Indiana, exact time unknown. According to the pilot's written statement, he was on the approach for the ILS runway 35 at Monroe County Airport, when the pilot sighted the runway at decision height (DH) and continued to land. The pilot used brakes and reverse thrust upon seeing the snow at the end of the runway but the airplane continued beyond the end of the runway. The pilot stated regarding how he could have prevented this accident by saying, "Not shoot approach with less than 1/2 mile visibility." A Federal Aviation Administration (FAA) Inspector said the pilot attempted to land after a missed approach with 1/8 mile visibility reported by the Control Tower. A Contract Controller reported airplane was 200-300 feet off the runway at mid-field of 6500' runway. The Contract Controller observed the airplane land long and skidded off the end of the runway, ending up about 200 yards off the end. The airplane went through a snowbank and about 6" to 8" of snow in the field at the end of the runway. The landing gear collapsed after leaving the runway environment. There were two airplanes ahead of this airplane that both went missed approach and diverted to their alternate destination. The FAA Inspector stated that there was some interest in going to the Indiana/Michigan Basketball game by the pilot and his employer. The U. S. Terminal Procedures for the ILS 35 approach, require a weather minimum of 200' and 1/2 mile visibility.