LOSS OF FREQ CHANGE HDOF IS A FACTOR IN A POTENTIAL CONFLICT BTWN A CITATION 650 AND AN UNKNOWN ACFT WHILE C650 WAS DSNDING TO 4000 FT OVER JOT; IL.

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DSNDING FOR ARR AT DPA; IFR ON AN IFR FLT PLAN. OUR FLT PLAN TOOK US OVER BOILER (BUT) VOR; THEN JOLIET (JOT) VOR; THEN DUPAGE. WE RECEIVED CLRNC TO DSND TO 4000 FT FROM THE CTR CTLR BEFORE WE HAD REACHED JOT. JUST PRIOR TO REACHING JOT VOR; WE RECEIVED A RELAY COM FROM AN X AIRLINES ACFT THAT CTR WANTED US TO CONTACT CHICAGO APCH. (CTR APPARENTLY DID NOT 'HAND US OFF' WHEN THEY WERE SUPPOSED TO.) WE CONTACTED CHICAGO APCH AND AT THE SAME TIME NOTED A 'TFC; TFC' ADVISORY ON OUR TCASII. SECONDS LATER; CHICAGO APCH ADVISED US TO MAKE AN IMMEDIATE R TURN; WHICH WE STARTED. AT THE SAME TIME; WE RECEIVED A 'CLB; CLB' RA (TCASII) WHICH WE ALSO COMPLIED WITH (CLBING R TURN). MOMENTS ALTER; WE RECEIVED A 'CLR OF CONFLICT' NOTIFICATION FROM OUR TCASII AND DSNDED BACK TO 4000 FT MSL AND ASKED CHICAGO APCH WHAT HDG THEY WOULD LIKE US ON. THEY GAVE US VECTORS ONTO DPA ILS RWY 2L AND THE FLT ENDED. I BELIEVE THAT WHAT CAUSED THE PROB WAS IMPROPER COORD BY THE CTR CTLR TO 'HAND US OFF' BEFORE WE GOT TOO LOW TO COMMUNICATE WITH HIM. ALSO; THE APCH CTLR 'SEEING US COMING' AND NOT TALKING TO US YET SHOULD HAVE VECTORED THE OTHER ACFT AWAY FROM THE CONFLICT SOONER. TO PREVENT A RECURRENCE; CTLR MUST ENSURE PROPER HDOF (CTR TO APCH) AND APCH CTLR NEEDS TO ENSURE SEPARATION OF TFC HE/SHE IS NOT TALKING TO BY VECTORING THE ACFT HE/SHE IS TALKING TO CLR OF THE CONFLICT BEFORE IT OCCURS.