Date: 201601
Local time of day: 1201-1800
Location: ZAU.ARTCC, IL
Light: Daylight
Aircraft: Medium Large Transport; Low Wing; 2 Turbojet Eng
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Descent
Airspace: Class A ZAU; Class E ZAU
ATC / advisory: Center ZAU
Reporter organization: Government
Reporter function: Enroute
Reporter qualification: Air Traffic Control Fully Certified
Human factors: Training / Qualification; Confusion; Situational Awareness; Communication Breakdown
Second reporter function: Enroute; Trainee
Anomaly: ATC Issue All Types; Airspace Violation All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Air Traffic Control Provided Assistance; Air Traffic Control Separated Traffic; Flight Crew Overcame Equipment Problem; Flight Crew Landed in Emergency Condition
Contributing factors: Procedure; Human Factors; Airspace Structure; Aircraft; Manuals
Primary problem: Procedure

Narrative: Sector X called and requested approval for Aircraft X descending to 10000 feet with a depressurization problem. I approved and coordinated with ZZZ Approach; as such an approval was eventually going into their airspace. The aircraft began a turn to the left which put him in conflict with another aircraft landing ZZZ in the opposite direction. Sector X called just after I had seen the turn and advised that Aircraft X was going to turn left to a 290 heading descending. I said with a left turn I could only release 21000 feet. To which the controller responded that Aircraft X had [requested assistance]. I then said if you're turning him now to a 290 heading; that puts him in Sector Y's airspace and Aircraft X is point out approved with me. I observed Aircraft X continue a sharp turn and steep descent; eventually leveling at 10000 feet. All the while; keeping the Front Line Manager informed of the ongoing situation.Minutes later; after the aircraft had leveled at 10000 feet in ZZZ airspace; Aircraft X broadcasted on my frequency and asks if he ever checked on. I said no; but to contact ZZZ Approach and gave him the frequency. I then talked to ZZZ Approach and they told me they knew nothing about the aircraft other than they had the handoff. I looked at the data block and the flight plan; and it still showed the original destination of ZZZ1. No altitude; heading or information had been coordinated nor had any approvals been made by ZZZ Approach by Sector X. There needed to be complete and clear communication between Sector X and all affected areas; and the Controller in Charge in Sector X needed to ensure that proper coordination had been accomplished with regard to a situation. None of this was done. After discussing it with all three controllers in that area consensus was; 'well; we shipped him to you.' However; I never expected him on frequency; as the last coordination I knew was that I had said 'point out approved.' I had no expectation of talking to the aircraft. He was in an extreme rate of descent and turning; the last thing the aircraft needed was multiple unnecessary frequency changes. Even if he did check on and I missed it while I was coordinating with the supervisor (as of this writing; I haven't listened to the recording yet so I don't know); I at least would have known that the coordination with ZZZ Approach would have been something for which I was responsible to ensure; as well as to look for the aircraft if I was expecting him on my frequency and I thought he had not yet checked on. All of this could have been avoided if one person responsible for Sector X had coordinated one of any of the omitted items of required information. Sector X never bothered to even tell me 'we shipped him to you' until after I was off position and walked into their area to find out what happened. Nor had anyone even informed ZZZ Approach that it was a [flight requiring assistance]; all ZZZ Approach knew was they took a handoff on an aircraft over ZZZ that was supposed to landing in ZZZ1; turning westbound with an altitude of 100 now in the flight plan. Thankfully; nothing happened.


Second narrative: [Report narrative contained no additional information.]


Synopsis: ZAU ARTCC Controller reported an aircraft with pressurization issues was vectored and descended into a TRACON's airspace without proper coordination.