Yem, first a couple of questions. Did this speaker work properly at some point as is? Was it previously replaced or repaired? If you can spend some modest bucks it's probably best to do the basket assembly replacement as ReignBass and Greenboy suggested. As I mentioned before it just looks wrong to me, like a manufacturing defect or something. I'm still assuming that the wire is smacking against the spider (you should double check this). If you want to play around a bit more, maybe you can try something like this:
Pardon my really crappy photoediting but I think you get the idea. The green patch is supposed to represent some kind of cement to hold the wire to the cone at that point and keep it well away from the spider.
Pardon my really crappy photoediting but I think you get the idea. The green patch is supposed to represent some kind of cement to hold the wire to the cone at that point and keep it well away from the spider.