What happened
The FAA’s narrative, in sentence case. The FAA writes it in capitals and removes private details.
On January 22, 2011, mem ARTCC reported an incident involving a loss of separation between cala 501 (B737-800) and N537DF (BE-400-A). Approximately 1220 UTC, cala 501 requested descent to a lower altitude due to a loss of cabin pressurization. Mem ATC cleared cala 501 initially to FL 350. During the step down to a lower altitude, mem ATC advised both cala 501 and N537DF of each others close proximity and location. N537DF was in a climb to FL340. Cala 501 requested to continue the descent to a lower altitude. Cala 501 acknowledged that it was an emergency situation. Mem ATC advised cala 501 that if they were declaring an emergency and had visual contact with N537DF, they could continue their descent. Both cala 501 and N537DF had visual contact with each other. Descending out of FL 340, both aircraft passed within 500 feet of others airspace. After passing, both aircraft continued on their route of fight without further incident.
As the FAA filed it
ON JANUARY 22, 2011, MEM ARTCC REPORTED AN INCIDENT INVOLVING A LOSS OF SEPARATION BETWEEN CALA 501 (B737-800) AND N537DF (BE-400-A). APPROXIMATELY 1220 UTC, CALA 501 REQUESTED DESCENT TO A LOWER ALTITUDE DUE TO A LOSS OF CABIN PRESSURIZATION. MEM ATC CLEARED CALA 501 INITIALLY TO FL 350. DURING THE STEP DOWN TO A LOWER ALTITUDE, MEM ATC ADVISED BOTH CALA 501 AND N537DF OF EACH OTHERS CLOSE PROXIMITY AND LOCATION. N537DF WAS IN A CLIMB TO FL340. CALA 501 REQUESTED TO CONTINUE THE DESCENT TO A LOWER ALTITUDE. CALA 501 ACKNOWLEDGED THAT IT WAS AN EMERGENCY SITUATION. MEM ATC ADVISED CALA 501 THAT IF THEY WERE DECLARING AN EMERGENCY AND HAD VISUAL CONTACT WITH N537DF, THEY COULD CONTINUE THEIR DESCENT. BOTH CALA 501 AND N537DF HAD VISUAL CONTACT WITH EACH OTHER. DESCENDING OUT OF FL 340, BOTH AIRCRAFT PASSED WITHIN 500 FEET OF OTHERS AIRSPACE. AFTER PASSING, BOTH AIRCRAFT CONTINUED ON THEIR ROUTE OF FIGHT WITHOUT FURTHER INCIDENT.