FLC OF CORP JET NOTICES FAST-RISING CABIN PRESSURE WHILE AT FL430 AND EXECUTES AN EMER DSCNT TO FL200 IN ORDER TO GET CABIN PRESSURE UNDER CTL. MAINT DISCOVERED LOOSE BLEED HOSE.

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THIS WAS A FLT FROM FXE TO MIDWAY. WE WERE CRUISING AT FL430 WITH A 6200 FT CABIN PRESSURE. PASSING JOHNN INTXN; WE WERE CLRED TO GO DIRECT BOILER VOR. WE THEN PROCEEDED OFF THE AIRWAY RNAV TO BOILER. ABOUT 200 MI S OF BOILER; THE CABIN ALT SUDDENLY STARTED TO RISE AT 6000 FPM OR MORE SINCE THE NEEDLE WAS AT THE STOP ON THE CABIN VIS. I IMMEDIATELY PUT ON MY OXYGEN MASK AND STARTED TROUBLESHOOTING IN ACCORDANCE WITH ACFT FLT MANUAL AND TRAINING PROCS; BUT; AS THE CABIN ALT WOULDN'T STABILIZE; WHEN IT REACHED 8500 FT; WE DECIDED TO EXECUTE AN EMER DSCNT. WE IMMEDIATELY NOTIFIED ZID AND SQUAWKED 7700; AND THEN MANUALLY DEPLOYED THE PAX OXYGEN MASKS AS A PRECAUTION SINCE OUR PAX WAS AN OLDER MAN AND WE WERE AFRAID THE CABIN ALT MIGHT KEEP CLBING FOR A WHILE. WE WERE IN VFR CONDITIONS AND HAD NOT SEEN ANY TFC AROUND US. THE CTLR IMMEDIATELY CLRED US TO FL250 AND THEN TO 10000 FT MSL. HOWEVER; WE WERE ABLE TO MAINTAIN A COMFORTABLE CABIN PRESSURE AT FL200; AND AFTER COMPUTING OUR FUEL ENDURANCE; DECIDED WE HAD ENOUGH RESERVES TO CONTINUE SAFELY TO MIDWAY AT THAT ALT. THE REST OF THE FLT WAS UNEVENTFUL. AFTER LNDG; MECHS WERE CALLED IN AND HERE IS WHAT THEY FOUND: THE ENG'S SUPPLY LINE JUST PRIOR TO THE FLOW CTL VALVE HAD COME LOOSE; CAUSING THE BLEED AIR TO DUMP INSIDE THE TAILCONE OF THE ACFT INSTEAD OF SUPPLYING THE CABIN WITH BLEED AIR. THERE IS NOTHING WE CAN THINK OF THAT COULD HAVE PREVENTED THIS FAILURE. THE LINE HAD GOTTEN LOOSE AND WAS LEAKING BLEED AIR; BUT IT WAS NOT DISCONNECTED; SO YOU COULD NOT POSSIBLY NOTICE THAT DURING VISUAL INSPECTION AT PREFLT.