A Center Controller reported an aircraft experienced a pressurization issue and descended below their assigned altitude.

Narrative

Aircraft Y departed ZZZ going to ZZZ1. The aircraft was climbing to 37000 ft. on a heading. I gave the aircraft direct ZZZ2 then came back and gave them direct ZZZZZ. It was a further turn to the east. The pilots didn't read back direct ZZZZZ and said 'standby' I asked if they had an issue and they said they needed to go back down to 35000 ft. I pointed the aircraft out the sector and let them know he was having an issue. The aircraft started to descend at a very high rate and was not responding. They leveled off roughly at 19000 ft. and I still could not hear the pilots. I could hear them intermittently and broken. I asked what the issue was and they said it was a stuck valve. The pilots did sound a little hypoxic and I told them to maintain 10;000 ft. The low sectors pointed the aircraft out to the adjacent sectors and approach control. The pilots initially wanted to continue on to destination but once they descended; they said they would divert to Indianapolis. They landed safely. Maybe try to figure out what was going on sooner; but I also did not have much time between them asking for lower and their rapid descent.