What was found
WE HAD TO MANUALLY SHUT THE LEFT ENGINE DOWN TO 616KK. ON DECENT THROUGH THE MID 30'S, WE BEGAN TO EXPERIENCE A LEFT ENGINE PRESSURE SWING VARYING BETWEEN OVER 100 PSI TO AS LOW AS 20PSI. AT THIS TIME, WE ELECTED TO REDUCE THE POWER ON THE LEFT ENGINE TO SEE IF IT WOULD STABILIZE, WHICH IT DID. INITIALLY, AS PILOT FLYING, I REDUCED THE LEFT THRUST LEVER TO JUST UNDER HALF POWER AND THE PSI LEVELED OUT MID TO HIGH 40'S. SHORTLY AFTER STABILIZING, IT BEGAN TO CONTINUE TO REDUCE TO THE LOW TO MID 20'S AND A CORRESPONDING LT OIL PRESS LOW CAS RED MESSAGE APPEARED. WE PROCEEDED TO RUN THE QRH CHECKLIST WHICH GAVE US THREE OPTIONS, NONE OF WHICH MATCHED THE LOW PSI AND TEMPERATURE WE WERE EXPERIENCING. AT THIS TIME DUE TO CREW DISCUSSION AND MATCHING THE QRH CHOICES AS BEST WE COULD, WE ELECTED TO DECLARE AN EMERGENCY AND MANUALLY SHUT DOWN THE LEFT ENGINE. WE LANDED IN MFE WITH NO ISSUE, WHICH WAS OUR FINAL DESTINATION FOR THE PASSENGERS.