WHEN THE PLT RECEIVED A WX BRIEFING AT 1012 CST, HE WAS ADVISED THAT THE WX AT HIS DESTINATION (FAYETTEVILLE, AR) WAS AN ESTIMATED 600' OVERCAST, VIS 4 MI WITH LIGHT DRIZZLE & FOG, BUT THE WX WAS FORCAST TO BEGIN TO IMPROVE IN ABOUT 1 HR.HE TOOK OFF & DURING ARRIVAL AT 1123, THE PLT WAS ADVISED THAT 2 PREVIOUS ACFT HAD MADE MISSED APPROACHES. AT 1139:17, HE WAS CLEARED FOR AN ILS APCH & INSTRUCTED TO REPORT OVER THE OUTER MARKER (OM). AT 1141:08, THE PLT REPORTED DEPARTINGTHE ELMIE INTERSECTION, 6.9 MI FROM THE OM. AT 1145:21, THE TOWER CLEARED THE ACFT TO LAND & REMINDED THE PLT TO REPORT AT THE OM. THE PLT RESPONDED, 'WAITING FOR IT.' ABOUT 30 SEC LATER, TOWER ASKED THE PLT TO REPORT IS POSITION, BUT THEREWAS NO REPLY. LATER, THE ACFT WAS FOUND WERE IT HAD CRASHED ON RISING TERRAIN (ELEV 1960') ALONG THE EXTENDED CENTERLINEOF RWY 16, ABOUT 7 MI SSE OF THE ARPT. THE MDA FOR THE APCH WAS 1800' (549' AGL). THE MARKER BEACON SW WAS FOUND IN THE OFF POSITION & THE GEAR & FLAPS WERE EXTENDED. THE ARPT ELEV WAS 1251' & ITS WX WAS: 500' OVC, 3 MI VIS, DRIZZLE, FOG.