From what I can see, this likely happend because of what others have stated, the cord was in poor condition and not taken care of. From what I can see, I suspect that the connection was loose at the soldering or so twisted it actually ruined part of the conductors. A fuse would not have likely not helped here. The increased resistance from a poor connection or too small of wires due to damage, will cause heat in the weakest point of the conductors or fuse ( if it had one), in this case it was the damaged part of the cable.Because the fuse should be sized for the wire, it would take a constant over current or dead short to burn the fuse out, but because the wire was very damaged, the wire at the burnt area is actually smaller now and weaker than the fuse. In a way, the cable acted like the fuse and burnt in half.