Firstly, the paper clearly explains that a userland (ring 3) process can easily discriminate between instructions that do not exist and instructions that the process lacks the credentials to execute simply because the two cases give rise to different exceptions (undefined and general protection, respectively).

Secondly, one could trivially log "I am going to try this" to a file, go ahead and do it, and if the machine crashes you consult the log and read exactly what was about to be done and evidently caused a hang. You don't necessarily need to write a log entry after doing something, in this case you can deterministically log what you are about to do and make deductions therefrom.

I'm sure there are ways to read out a CPU Hang and reset if that happens, if necessary via external hardware^(I'm guessing)^(I don't actually know)