THE FLT WAS CLEARED FOR A NIGHT ILS APCH & ADVISED THAT TWR AT DEST HAD CLOSED. TWR HAD RPTD AT CLOSING THAT FOG WAS FORMING & THE FLT WAS ADVISED OF THE FOG. THE ACFT WAS LOCATED ON A REMOTE PART OF THE ARPT THE NEXT MORNING. THE ELT HAD ACTIVATED BUT THE SIGNAL WAS WEAK DUE TO CRASH DAMAGE. PAX SAID THEY NEVER SAW RWY LIGHTS, ONLY TAXI LIGHTS, & THAT PLT ATMPTD TO PERFORM A GO-AROUND. GEAR WAS RETRACTED & ACFT HIT LEVEL GRASSY AREA IN A NEAR LEVEL ATTITUDE. THE PLT WAS NOT WEARING A SHOULDER HARNESS. THE PAX CROUCHED IN THE AISLE NEXT TO THE PLT, HELPING HIM FIND THE RWY, NOT WEARING RESTRAINING BELTS. NO PUBLISHED APCH PLATE FOR ILS PROC FOR THAT RWY WAS FOUND IN ACFT. TOX REPORT REVEALED PLT HAD 3 MCG/ML DEXTROMETHORPHAN, AN INGREDIENT FOUND IN OVER COUNTER COLD REMEDIES. ACCORDING TO REPORT, LEVELS OF THAT SUBSTANCE IN BLOOD GREATER THAN 0.1 MCG/ML WAS SUFFICIENT TO CAUSE DROWINESS.