A KING AIR PLT AND INSTRUCTOR LANDED ON A CLOSED RWY AT DDC PRACTICING A SINGLE ENG APCH.

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WHILE ON A MULTI-ENG TRAINING MISSION WITH A NEWLY HIRED PLT; I WAS OPERATING AS A COMPANY PLT TRAINER/CHK AIRMAN NEEDING TO HAVE DEMONSTRATED TO ME 2 ILS APCHS; INCLUDING A SINGLE-ENG APCH TO A LNDG. THE WINDS AT GBD; GREAT BEND; KS; BECAME A TAILWIND PRECLUDING LNDGS FROM AN ILS STRAIGHT-IN AT GBD; SO I DIVERTED THE STUDENT TO DDC; WHICH HAS AN ILS INTO THE CURRENT WIND. DDC ASOS VERIFIED VFR WX WITH SUITABLE WIND FOR ITS ILS. NOT HAVING PLANNED TO USE DODGE CITY; I DID NOT CHK NOTAMS ON THE GND PRIOR TO TKOF. I DIDN'T CALL THE FSS TO CHK NOTAMS UPON DECIDING TO DIVERT ON SHORT NOTICE. UPON FINDING OUT THE ILS WAS NOT IN SVC UPON ARR; I SWITCHED THE TRAINING APCH TO A VOR STRAIGHT-IN TO RWY 14 SIMULATED SINGLE ENG. (LACK OF AN ILS SIGNAL SHOULD HAVE BEEN A CLUE THAT THE RWY MIGHT BE CLOSED.) FROM THE AIR ON SHORT FINAL THE RWY LOOKED UNOBSTRUCTED. AT THE SAME TIME THE STUDENT PUT DOWN FULL FLAPS (WHICH IS A COMMITMENT TO LAND WITH AN ACTUAL ENG OUT LNDG. WE WERE SIMULATED ENG OUT WHICH WOULD REQUIRE A RISKY GAR). ON SHORT FINAL; I NOTICED A LARGE CLOTH OR CANVAS 'X' PANEL PAINTED YELLOW; OFF OF THE RWY SURFACE BTWN THE THRESHOLD AND THE FIRST APCH LIGHT POST. THE 'X' MARKING WAS NOT ON THE RWY BUT IN THE DIRT. NO OTHER 'X' MARKINGS WERE IN VIEW FROM THAT POINT OF VIEW. AS WE WERE IN A SINGLE ENG LNDG NEAR TOUCHDOWN; I MADE THE LAST SECONDS AVAILABLE TO CONCLUDE THAT; SINCE THE 'X' PANEL WAS IN THE DIRT OFF OF THE RWY; NO OTHER MARKERS WERE IN SIGHT; AND NO WORKERS WERE IN SIGHT; THE RWY WAS OPEN BECAUSE IT WAS SUNDAY AND NO WORKERS WERE AROUND. AFTER AN UNEVENTFUL LNDG; A BARRIER ACROSS THE FAR DEP END CAME IN VIEW; AS WELL AS BARRIERS THAT BLOCKED ACCESS FROM THE TXWYS NEAR THE INTXN OF RWY 2/20 AND RWY 14/32. IT BECAME OBVIOUS; DUE TO THE BARRIERS; NOT OBVIOUS DUE TO 'X' MARKINGS ON THE ARR END OF RWY 14; THAT THE RWY WAS CLOSED. WE TAXIED CLR OF THE RWY ONTO A TXWY THAT HAD A BARRICADE BTWN US AND THE TXWY TO RWY 2/20 WHICH WAS OPEN. I LINEMAN SAW OUR PREDICAMENT AND MOVED PART OF THE BARRICADE WHICH ALLOWED US TO TAXI TO THE OPEN RWY AND DEPART. NO OTHER ACFT; VEHICLES; OR PERSONS WERE SEEN OR HEARD. UPON ARRIVING AT HOME BASE; NOTAMS WERE CHKED AND FOUND TO HAVE BEEN PUBLISHED TO ANNOUNCE THE RWY CLOSURE. I CANNOT ASSUME A VFR ARPT ON A NICE DAY DOES NOT HAVE NOTAMS. I MUST CHK EVERY TIME. I WAS NOT UNDER THE IMPRESSION THAT AN 'X' OFF OF THE RWY SURFACE WAS A PROPER 'CLOSED' MARKING. HAD I CHKED FOR NOTAMS FIRST; I WOULD HAVE KNOWN THAT THE BARRICADE WAS INTENDED TO MEAN THAT THE ENTIRE RWY WAS CLOSED. I GUESS THAT THE GOOD TO COME OF THE MATTER WAS THE INSTRUCTIONAL VALUE TO BOTH OF US. I HAVE A 30+ YR CAREER WITH NO ACCIDENTS; INCIDENTS; VIOLATIONS; OR EVEN FELT THE NEED TO FILE A NASA RPT PRIOR UNTIL NOW. I WAS EMBARRASSED; HUMBLED; AND THANKFUL OF NO PROBS CAUSED BY LNDG ON A CLOSED RWY.