WHILE FLYING NORTHWEST OVER WATER ALONG THE PACIFIC COAST ON AN IFR CLNC, THE PLT RPRTD TO THE SECTOR CONTROLLER (CTLR) 'WE'VE GOT A PROBLEM.' THE CTLR INQUIRED ABOUT THE NATURE OF THE PROBLEM. THE PLT THEN STATED, 'GOING DOWN FAST, OUT OF CONTROL.' THE CTLR OBSERVED THAT THE ACFT WAS LOSING ALT RAPIDLY & INSTRUCTED THE PLT TO TURN RIGHT TO 090 DEG FOR VECTORS TOWARD THE SHORELINE; THE PLT RESPONDED, 'WE'RE GOING IN.' NO FURTHER TRANSMISSIONS WERE RECEIVED FROM THE PLT. THE CTLR NOTED THE ACFT'S TRANSPONDER CODE WENT INTO A COAST MODE & THE PRIMARY TARGET WENT INTO A SLOW LEFT TURN. RADAR CONTACT WAS LOST WITH THE ACFT AFTER IT HAD TURNED TO A SOUTHWESTERLY HEADING. COAST GUARD HELICOPTERS ARRIVED OVER THE AREA OF THE ACDNT AT ABOUT 1700 PST. THE HELICOPTER AIRCREWS FOUND AN OIL SLICK, A LNDG GEAR & OTHER REMNANTS OF THE ACFT; HOWEVER, THE MAJOR PORTION OF THE ACFT SANK & WAS NOT RECOVERED.