I can only talk from first hand experience regarding the PPL. The detailed training I received regarding such things as a control failure, involved checking the little nut that held the anti-servo tab mechanism in place was properly fastened (as part of the pre-flight inspection), because if it came off you'd get a severe control flutter and the aeroplane would probably break up. I was also cautioned regarding loose items in the cabin (coins, tools, pens etc) that, if left behind, could possibly find their way into a control run and jam something.
I was also told that if I froze on the controls, locking them in place at a critical juncture of flight, that I would find out (briefly) the secondary function of the crash axe.
A friend who went through rudder hardover training once the issue was discovered - it was type/actuator specific - told me that following this training that if a rudder hardover occured on his flight below about 10,000 feet, he was extremely confident that he would die.
Hope that helps.