CTLR DESCRIBED LOSS OF SEPARATION AT FL280 INVOLVING AN ACFT WITH PRESSURIZATION PROBS IN AN EMER DSCNT.

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ACFT X WAS CLBING W. ACFT Y WAS BEING STEPPED UP BELOW HIM; 7 MI BEHIND AND 40 KTS FASTER. ACFT X ADVISED THEY NEEDED TO DSND TO FL240. RADAR CTLR ASKED IF THEY WERE AN EMER. ACFT X REPLIED 'YES SIR.' THEY WERE ISSUED A TURN AND TOLD TO STOP CLB AT FL300. THE ACFT DID NOT REPLY. THEY CONTINUED ON ASSIGNED RTE. THE ALT STOPPED AT FL295 AND STARTED DROPPING. THE RADAR CTLR ASSIGNED FL280 (ACFT Y WAS CLBING THROUGH FL265). COM WAS STILL NOT ESTABLISHED. THE SECTOR CTLING ACFT Y WAS TOLD TO TURN ACFT Y OUT FROM UNDERNEATH ACFT X. THE TURN KEPT THE ACFT AT LEAST 3 MI APART AS ACFT X DSNDED TO FL240. COM WAS REESTABLISHED AND ACFT X ADVISED THEY HAD A PRESSURIZATION PROB AND WERE HAVING TROUBLE CTLING THE ACFT. THEY WERE GIVEN CLRNC BACK TO ZZZ AND 19000 FT. I BELIEVE ALL PERSONS INVOLVED ACTED IN AN EXEMPLARY MANNER. THE PLTS DID WHAT THEY HAD TO DO TO CTL THE ACFT. MY RADAR CTLR WAS QUICK TO RECOGNIZE THAT ACFT X WOULD BE MAKING A DSCNT WITHOUT CLRNC AND TOOK QUICK AND ACCURATE MEASURES TO AVOID A MIDAIR COLLISION. SUPPLEMENTAL INFO FROM ACN 703423: WHILE CLBING TO CRUISE ALT; WE RECEIVED AURAL AND VISUAL WARNINGS THAT PRESSURIZATION HAD FAILED. ACCORDING TO THE EMER CHKLIST; WE IMMEDIATELY INITIATED A DSCNT THEN DECLARED AN EMER WITH ATC. WE RETURNED TO ZZZ WITHOUT FURTHER INCIDENT AND MADE A NORMAL LNDG. ATC ADVISED OF A POSSIBLE LOSS OF SEPARATION. THERE WAS NO TA OR RA. OUR CORPORATE MAINT STAFF DETERMINED THAT THE PRESSURIZATION CTLR FAILED.