I tried looking up the DEK engine and didn't find much. The pictures do suggest that it might be made by the same company that makes the Greyhound and Predator engines that some of us have. Those engines are Honda clones which means that Honda parts may often be replacement parts.

Your description is somewhat unclear but I would guess that you are describing a broken spark plug insulator (the white part of the plug) and broken spark plug wire connector (the part inside the rubber boot end of the plug wire). It also seemed you were suggesting that the spark plug was partially unscrewed into the engine. I don't know about the melting description.

I suspect that you could replace the plug wire with some generic Honda or similar wire. You would need to remove enough housing to follow the wire to the coil connection on the engine. Remove wire and take to lawn mower shop. I suppose the best way to find a replacement plug assuming the number is missing on the plug, is to see what plug is on a new chipper at HD. If I am mistaken about disintegrated insulator, just replace the plug (although then I don't know what the white stuff is).

I would say the white stuff is the insulator material. My concern is that it got hot enough to melt anything. I know I have burned my hand through my glove on the exhaust grid. So something gets very hot. I will check with HD and see what they have on the new ones. Thank you.