NEAR GND COLLISION WITH A PA32 PVT PLT APCHING AND LNDG ON AN OCCUPIED RWY AT MYAM; FO.

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WX CLEAR ABOUT 50 MI VISIBILITY; FEW CLOUDS AT 3000 FT; WINDS FAVORING RWY 27 AT MHH. PRIOR TO ARR AND ATC RELEASE; ATC NOTIFIED US OF AN ACFT ALSO HEADING TO MHH AND THAT WE WERE OVERTAKING IT. WE PICKED THE ACFT UP ON TCASII AND SAW IT WAS NO FACTOR. DURING OUR INITIAL CALL FOR A GENERAL TA; WE GOT NO RESPONSE FROM THE PIPER; BUT DID ON THE SECOND WHEN WE CALLED R DOWNWIND. THE PIPER CALLED A L DOWNWIND AND WE BOTH CONFIRMED VISUAL ON EACH OTHER. THERE WAS 1 ACFT ON THE GND. I AM NOT SURE; BUT THINK IT WAS A SMALL EXECUTIVE JET. THEY RESPONDED AND SAID THEY WOULD HOLD TO ALLOW US TO LAND. WE PROCEEDED WITH OUR LNDG SINCE WE WERE FAR AHEAD OF THE PIPER ACFT. I BELIEVE WE WERE TURNING BASE AS THE PIPER WAS ENTERING THE END OF ITS DOWNWIND LEG. THE LNDG WAS UNEVENTFUL. DURING TAXI BACK; THE PIPER CALLED BASE TO FINAL. I NOTIFIED THE PIPER WE WERE TAXIING BACK; AND GOT NO RESPONSE. THEN BOTH CAPT AND I SAW THE PIPER ON FINAL. WE BOTH KNEW WE HAD A PROB; AND REALIZED THE PIPER WAS GOING TO LAND WHILE WE WERE STILL ON THE RWY. CAPT FIRST TRIED TO EXPEDITE OUR TAXI BACK; BUT SOON REALIZED WE HAD NOWHERE TO GO. CAPT CALLED FOR THE GAR. I CALLED FOR THE GAR AGAIN WITH THE PIPER'S RESPONSE; 'I AM A LITTLE BUSY RIGHT NOW.' I FLASHED OUR LNDG LIGHTS AND THE PIPER CONTINUED TO DSND. FINALLY; CAPT FOUND A SMALL TXWY AND WE MANAGED TO CLR THE RWY IN TIME FOR THE PIPER TO LAND. IT IS MY OPINION THAT IF WE DID NOT FIND THAT TXWY; THERE WOULD HAVE BEEN A COLLISION. AFTER SOME EFFORT TO GET THE PLANE TURNED AROUND; WE GOT BACK TO THE TERMINAL AND DISEMBARKED THE PAX. CAPT WENT TO RPT THE INCIDENT AND I WENT TO TALK TO THE PLT. SHE IDENTED HERSELF AS A PVT PLT. I ASKED WHY SHE DID NOT RESPOND AND CONTINUED TO LAND. SHE SAID SHE THOUGHT THAT THERE WAS A TXWY AND THOUGHT WE WERE VACATING. I EXPLAINED THERE WAS NONE AND THEN ASKED IF SHE HAD FAMILIARIZED HERSELF WITH THE ARPT AND ADMITTEDLY SHE HAD NOT. SHE THEN GOT BELLIGERENT AND BROKE OFF THE CONVERSATION. I ALSO OBSERVED; BUT COULD NOT VERIFY; THAT THE PLANE APPEARED OVERLOADED WITH AN AFT CTR OF GRAVITY.