To be honest we provide enough genuine mistakes that have to be managed....
But, they do have pilots drop dead every now and then, mostly at very inconvenient times. My last death was in the middle of rotate at Hong Kong yesterday. FO carried on, playing both roles. I miraculously recovered to do the overweight landing, but in the real world he would have just done the same.
There have been some specific exercises to show the aircraft reaction to some mistakes. Retraction of the flap, instead of the gear, just after take off was looked late last year. As the flap starts to retract, the angle of attack increases, and the system stops the retraction. Quite impressive, as it just flew away with only a slightly degraded climb gradient.
The sessions are not random. Instructors need to remain within a fairly tight script to ensure that the standardisation of the training programmes works. Nevertheless, there are enough permutations, that no two sessions are quite alike. Yesterday, our instructor wanted to give us a comms failure (which is quite difficult in an aircraft with so many different means of communications), and he found a method he hadn't tried before....and it stopped us in our tracks, in that there was no cure, and it wasn't totally unrealistic.