ACR X HAD NMAC LTSS FROM SMT Y. EVASIVE ACTION TAKEN. SYS ERROR.

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N90 VECTORS ACR X H/IL86; FOR THE ILS TO RWY 31R. ACR X CHKS IN AND I ADVISE HIM HE'S FOLLOWING A WDB 5 MI AHEAD. THE WDB LANDS AND I INSTRUCT HIM TO EXIT THE RWY AND TO TAXI ON TO 'W' TXWY AND CONTACT GND. THE WDB TURNS AND STOPS; STILL ON RWY. I INSTRUCT THE WDB TO MOVE AWAY FROM THE RWY AND TO TAXI ON TO THE OUTER AND CONTACT GND. I WATCH UNTIL THE WDB CLRS THE RWY. WHEN I LOOKED BACK AT THE D-BRITE; I SEE THAT SMT Y; VFR; SMT Y HAD BEEN VECTORED RIGHT IN FRONT OF ACR X WITH ACR X GOING APPROX 80-100 KTS FASTER. NO HDOF NOR COORD WAS AFFECTED ON N90'S PART. I ADVISED ACR X TO CONTINUE; AND THEN ATTEMPTED CONTACT WITH SMT Y TO TURN HIM OUT; BUT SMT Y WAS NOT ON FREQ. CAB COORDINATOR ADVISED N90 THAT WE NEED TO TALK TO SMT Y AND THEY REPLIED THAT THEY WEREN'T TALKING TO HIM. SMT Y IS NOW OVER THE APCH END OF THE RWY; APPROX 900 FT DSNDING; WITH ACR X VERY CLOSE BEHIND AND LOW. A GAR TO ACR X AT THIS TIME WOULD HAVE HAD HIM CLBING INTO THE SMT Y DSNDING CAUSING A MIDAIR; A L TURN WOULD HAVE ACR X CRASH INTO THE CTLR TWR; AND A R TURN WOULD TAKE HIM INTO LGA'S AIRSPACE. I WAITED UNTIL THE SMT Y WAS OVER THE DISPLACED THRESHOLD APPROX 75 FT ON FINAL WHEN I ISSUED THE GAR TO ACR X WITH A R TURN; COORD WITH LGA WAS AFFECTED. ACR X PASSED OFF THE SMT Y R SIDE AT A VERY CLOSE PROX. SMT Y ADVISED FREQ CHANGE TO TWR WAS ISSUED AS HE WAS FLARING OUT OVER THE RWY. RESOLUTION; N90 FINAL CTLR TO ALWAYS HAVE AN ASSISTANT OR COORDINATOR PRIOR TO WORKLOAD BECOMING OVERWHELMING THEREBY CAUSING INCIDENTS STATED.