Sophisticated Auto Flight systems available on modern aircraft can include and Auto Descent option, which will automatically engage if the cabin pressure raises above 14,000 feet. The autopilot commands a 90% left turn (to clear potential traffic on designated air routes), auto throttles simultaneously would reduce to idle. The flight level change (FLC) is engaged and speed is selected to maximum. This causes the aircraft to initiate a maximum descent rate with auto level off at usually around 14,000. It would be interesting to note the distance time between the radar blips (to determine the ground speed) after the aircraft made the left turn to determine its speed which would be about 2/3 of normal cruise speed if it descended.
A catastrophic failure of the pressurization vessel could have also affected power to some electrical busses and caused the transponder to not function.