F100 CREW HAD AN NMAC WITH AN ACFT OPERATING IN IMC WITH NO ATC CTL.

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NMAC AT DSM. WE WERE BEING VECTORED FOR THE ILS RWY 13 AT DSM. THE WX WAS 500 FT OVCST 1 SM; LIGHT RAIN SHOWER. THE TOPS WERE AT 13000 FT. WE WERE CLRED OUT OF (I BELIEVE) 7000 FT FOR 3000 FT. VECTORED TO BASE LEG. WE WERE ADVISED THAT THE CTLR WAS GOING TO VECTOR US IN FRONT OF TFC IN THE LCL AREA. I SAW THE TFC ON MY NAV DISPLAY VIA THE TCASII. HE WAS IN FRONT TO THE L BELOW AND CLBING. WE WERE DSNDING. I BECAME INCREASINGLY CONCERNED AS THE TFC APPEARED TO BE CLOSING ON OUR POS. WHEN WE WENT THROUGH 4000 FT; THE OTHER ACFT CONTINUED TO CLOSE ON US. I TOLD MY FO (PF) TO CLB AND GET AWAY FROM HIM AT THE SAME TIME THE TCASII ALERTED WITH AN RA. THE OTHER ACFT CAME WITHIN 400 FT OF US AND APPEARED VERY CLOSE LATERALLY. AFTER THE RA WAS COMPLIED WITH; WE RETURNED TO THE DSCNT AND DOGLEG TO FINAL. THE REST OF THE APCH WAS UNEVENTFUL. THE CTLR SEEMED SURPRISED WHEN I EXPRESSED MY DISPLEASURE WITH THE VECTOR. UPON TALKING TO HIM ON THE GND; I WAS THE ONE WHO WAS SURPRISED WHEN THE CTLR TOLD ME THAT THE OTHER ACFT WAS SQUAWKING VFR (AN IMPOSSIBILITY GIVEN THE WX CONDITIONS) AND THAT HE HAD NOT BEEN TALKING TO HIM; ONLY VECTORING ME AROUND HIM. HE MAY HAVE TOLD ME THAT EARLIER IN THE APCH; BUT I DON'T THINK SO; AS I WOULD HAVE REALIZED THERE IS NO WAY HE COULD HAVE BEEN MAINTAINING VFR IN THOSE CONDITIONS. I BELIEVE THE OTHER ACFT MADE A TURN TOWARDS US AND THE CTLR DIDN'T RECOGNIZE IT UNTIL WE CONFLICTED. IN HINDSIGHT; I SHOULD HAVE STATED MY INTENTION TO FILE AN NMAC; BUT I WAS FLUSTERED AND WAS MORE INTENT ON JUST GETTING SAFELY ON THE GND. NEXT TIME; I DON'T BE SO COMPLACENT WITH AN OBVIOUS DEVELOPING SCENARIO. SUPPLEMENTAL INFO FROM ACN 564045: WE HAD BEEN IN THE WX FROM ABOUT 13000 FT AND WERE EXPECTING TO BREAK OUT ABOUT 1400 FT MSL (500 FT AGL) BASED ON THE ATIS WHICH HAD BEEN RECENTLY UPDATED. WE NOTICED THAT WE WEREN'T DIVERGING FROM THE TFC AND THE CAPT TOLD ME TO BE READY TO CLB IF IT DIDN'T RESOLVE ITSELF. IT APPEARED THAT WE WOULD NOT PASS IN FRONT OF THE TFC AND THE CAPT DIRECTED ME TO CLB. AS I INITIATED THE CLB; WE RECEIVED AN RA FROM THE TCASII TO CLB. I CONTINUED THE CLB AND COMPLIED WITH THE RA. AT THE CLOSEST POINT; THE TCASII SHOWED THE TFC 400 FT BELOW US WITH NO DISCERNIBLE LATERAL SEPARATION. THE CAPT CONVEYED HIS DISSATISFACTION WITH THE AVOIDANCE VECTOR TO APCH WHILE WE WERE STILL AIRBORNE. THE CAPT TALKED TO A SUPVR AND THE CTLR WHO WAS VECTORING US. MUCH TO MY SURPRISE HE WAS ADVISED THAT THE TFC HAD BEEN SQUAWKING VFR AND THE CTLR WASN'T EVEN TALKING TO HIM. THE WX OBVIOUSLY MADE VFR FLT ILLEGAL. THE CAPT WAS UPSET WITH HIMSELF THAT HE WASN'T A LITTLE MORE PROACTIVE ABOUT THE SIT. APCH CTL LEFT OUT A KEY PIECE OF INFO ABOUT THE TFC -- THAT IS WAS SQUAWKING VFR. WE WORKED TOGETHER AS A CREW AND LIKELY AVOIDED A FATAL OUTCOME.