Enroute Air Traffic Controller reported working an aircraft that was experiencing pressurization problems resulting in the aircraft making a rapid descent and they gave control of this aircraft to another sector.

Narrative

I was working Sector XX and Sector XY together. Traffic volume was low to medium; but the amount of aircraft needing to deviate was elevated. Every aircraft was asking about the rides; which were light to moderate chop all altitudes FL400 and below. In the midst of giving clearances an aircraft Requested Priority Handling. I was able to ascertain the aircraft was Aircraft X. The language barrier was a factor in our communication. I could hear they audibly shaken and needed help. They asked for descent immediately and I was able to provide them with my lowest altitude I owned which was FL240. They were level at FL300 at the time. It appeared that Aircraft X turned approximately 40 degrees to the right without a clearance. I immediately called Aircraft Y with an pointout down to 110 which was approved. After I looked back at the data block Aircraft X was already down to FL255 and descending rapidly. My initial thought was this plane is in an uncontrolled descent and they might crash. The VRI was indicating -5800. I told the plane to descend and maintain 110. I coordinated with Aircraft Y again asking for 100 to help them with pressurization because that is what I thought was the problem. Aircraft Y agreed to the pointout and released total control of the aircraft. I asked Aircraft X for nature of the flight and they were too busy to tell me. Our low side controller had little to no planes so he yelled out that he can work him and called radar. I made sure Aircraft X needed no immediate further assistance from me. Aircraft X responded in the negative and then I switched him to Sector XZ on XXX.X. The receiving controller eventually told me it was a dual engine bleed failure and the oxygen masks had deployed.