C182 ON SHORT FINAL CONDUCTING IFR ILS RWY 23 APCH TO FDK IS SURPRISED TO HEAR AND OBSERVE ANOTHER C182 DEP FROM RWY 23; REPORTEDLY ON AN IFR CLRNC.

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I WAS ENRTE TO FDK; MD. I WAS BEING VECTORED BY POTOMAC APCH FOR THE ILS RWY 23. I INTERCEPTED THE LOC APPROX 15 MI OUT. ABOUT 12 MI OUT; POTOMAC APCH RPTED OUR POS; CLRED US FOR THE APCH; STATED; 'RADAR SVC IS TERMINATED; SWITCH TO ADVISORY FREQ; RPT CANCELING IFR IN THE AIR OR ON THE GND ASAP.' MY COPLT ACKNOWLEDGED AND SWITCHED TO 122.725. HE MADE 3 RADIO CALLS ON THE 122.725 AT 10 MI; 5 MI; AT 1 MI STATING WE WERE ON THE ILS; THE ARPT; OUR CALL SIGN AND THE DISTANCE. JUST BEFORE WE BROKE OUT; AN UNIDENTED C182 CALLED ON THE FREQ STATING HE WAS DEPARTING FDK RWY 23 IFR. MY COPLT STATED AGAIN WE WERE LESS THAN 1/2 MI OUT AND THE OTHER PLT DID NOT ACKNOWLEDGE. AS SOON AS WE BROKE OUT; WE COULD SEE THE OTHER ACFT BEGINNING ITS TKOF ROLL. I SLOWED OUR ACFT DOWN AND LANDED BEHIND THE OTHER ACFT RIGHT AFTER IT LEFT THE RWY. AFTER WE CLRED THE RWY; WE CONTACTED POTOMAC APCH ON 126.900 STATING WE WERE ON THE GND AND CANCELING IFR; AS WELL AS THERE WAS ANOTHER ACFT TAKING OFF. THEY SEEMED SURPRISED TO HEAR FROM US; BUT NOT VERY CONCERNED ABOUT THE OTHER ACFT. IT APPEARS EITHER OF 2 THINGS HAPPENED: EITHER THE OTHER ACFT TOOK OFF WITHOUT AN IFR CLRNC; OR APCH FORGOT ABOUT US AND ISSUED 2 ACFT IFR CLRNCS IN THE SAME AIRSPACE WITHOUT RADAR COVERAGE. SINCE THE CEILINGS WERE CLOSE TO MINIMUMS; IF I WENT MISSED APCH; I WOULD HAVE BEEN HEADING THE SAME DIRECTION AS THE OTHER ACFT IN IMC WITHOUT ANY IDEA WHERE HE WAS; A DANGEROUS SITUATION TO SAY THE LEAST.