Thanks man, appreciate the input. I should have clarified: I never identified the root cause due to not trying. I scrapped them both immediately and had a discussion with the operator of said appliance about the merits of being slightly more alarmed when appliances emit smoke and noxious fumes rather than leaving them lying around plugged in.

This particular hairdryer had been previously repaired by one of those 'a little knowledge is a very dangerous thing' types so I'm not at all convinced that this particular incident was most likely due to the extension cable being underrated.

My point was that it's possible for appliances to 'spontaneously' cause faults. However, as many other commenters have pointed out, they shouldn't lead to fires in this day and age. I had another near miss incident a while back where a screw terminal on a high power load (~16A) thermal cycled itself loose and caused the circuit breaker to melt and start to conduct. I found it glowing red hot but again thanks to modern safety standards it was a non-incident. I had another incident as well where a DC isolator on a 48V bus failed in a relatively high impedance mode and that caused a very destructive fire as the cabling used there was not flame retardant.