Continued...
I think there are some further observations which can be take from the photoof the plug in #31 and a comparison of it with the 'new' plug image.
Although there is the image of the oblong outline of the perimeter of the fuseholder, there is no shading one might expect for the peep hole if the removable fuse carrier was in place - I think this is significant hence my question to the OP.
We also don't see any overheating of the internal parts or surfaces of the double socket. All heating effects were localised and external and close to the fuse assembly.
If one looks carefully at the underside of the plug I think one can see some tracking from the load end of the fuse to the earth pin and also towards the earthed socket securing screw on the left.
There are signs of arc spatter on the surface of the socket near the neutral pin entry.
The supply end of the fuse carrier was hottest because of the browner scorch mark.
The OP does not state it but I infer because he has not that in the lead up to this event the dryer was working normally and had been on earlier occasions.
In sum without over labouring things too much further, I reckon the fuse was not securely in place nor protected against ingress of contaminents. As a result the connections between the fuse end caps and the fuse clips were prone to becoming dirty. We suspect too that the clips may not have been that tight on the end caps or the fuse not fully home in them. Over time localised Ohmic heating led to oxidation and then arcing. The heat these generated caused the plastic around the metal of the fuseholder to decompose into carbon products which are conductive.
There is a strong electric field between the fuse carrier live parts and the earth pin of the plug and also the earthed socket securing lug. Over time this field attracted hot ionised material which became deposited as two tracks - I think you can see one between the load end of the fuse and the earth pin along the perimeter of the fuse assembly (and also along the crack on the faceplate of the socket under the earth pin entry going north-west/south-east. Very quickly the conditions were created for
dry arcing and the gap between the underneath of the plug and the surface of the socket acted like an
arc chute, containing and channeling arcing between the live parts and the earth pin and earthed screw hole.
This I think is what the OP's wife had to deal with. I also think their home does not have RCD protection and I would not be surprised to hear it has rewireable fuses.
After a google search I turned up this piece from the US:
The Basics of Electrical Overheating - http://www.ecmweb.com/ops-amp-maintenance/basics-electrical-overheating
All, I am suggesting then is the OP may have experienced the effects of dry arcing on the underside of the plug. An arc of course if highly conductive and large currents can flow through them, remembering that the peak to peak voltage swing is +350V to -350V.
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