DRG A NIGHT ARRIVAL, THE PLT WAS CLEARED FOR AN ILS RWY 4 APCH AFTER BEING ADZD THE SKY WAS PARTIALLY OBSCURED, MEASUREDCEILING 200' OVERCAST, VIS 1/2 MI WITH FOG, WIND 080 AT 17 KTS. MINS FOR THE APCH WERE 200' CEILING & 1/2 MI VIS. THE PLT WAS CLEARED TO BEGIN THE APCH FROM A 7 MI DME ARC. AS THE ACFT DESCENDED ON THE APCH, RADAR CONTACT WAS LOST & THE PLT WAS CLEARED TO CONTACT QUINCY RADIO. AS THE PLT RPRTD PASSING THE QUINCY VOR (JUST SHORT OF THE ILS OUTER MARKER/FINAL APCH FIX), THE FSS SPECIALIST ADVISED HIM THE VIS HAD DROPPED TO 3/8 MI. AFTER THE PLT RPRTD PASSING THE OUTER MARKER, RADIO CONTACT WAS LOST, EXCEPT FOR THE SOUND OF A KEYED MIKE. SUBSEQUENTLY, THE ACFT HIT TREES & CRASHED WELL LEFT OF THE ILS CENTERLINE, APRX 3/10 MI WEST FROM THE APCH END OF RWY 4. NO PRE-ACDNT MALFUNCTION OR FAILURE OF THE ACFT OR ILS FACILITY WAS FOUND.