How often has this happened on the B737 family?
Have certainly witnessed this type of event in the 737 Classic simulator. During re-current training the instructor failed the clutch motor on the No 1 thrust lever during a clean descent on a DME arc at idle power. The autopilot and autothrottle were engaged at the time. As the aircraft decelerated in level flight and extended gear and flaps just before ILS glide path intercepted, the No 2 engine increased thrust to almost 80% N1 while the No 1 thrust lever stayed at idle. The aircraft was by then coupled to the ILS.
The control wheel was 45 degrees off centre but the crew seemed oblivious to the increasingly dangerous situation. When the simulator instructor dropped the hint that 45 degrees wheel angle coupled with huge throttle split was unusual, the captain muttered a exclamation and called for the engine failure and shut down checklist for the "failed" engine. At the point the automatic pilot gave up the ghost and the aircraft rolled into a steep spiral dive left and reached 60 degrees angle of bank and ten degrees nose down before the simulator instructor "froze" the simulator to discuss that situation.
Neither pilot did anything to correct the situation and the captain kept calling for the QRH engine failure checklist but without taking any action to prevent the aircraft rolling into the ground. There was nothing wrong with the engine and all he needed to do was restore equal power by pushing No 1 thrust lever open since it was only the clutch motor that wasn't working.
The airline was mainland Chinese. Indications were that ethnic culture was probably involved as the co-pilot watched the whole drama evolve without a word. . .