Why do my Christmas lights have a white polyester filament inside the thin rubber wire?
The filament is there to add strength to the cord. Everything else stretches more than the poly-fiber so when you pull on it(the cord) it strains against the fiber instead of the delicate electrical connections. As far as splicing it goes...you could tie a knot in it if there's enough slack or just ignore it and be careful with that spot in the future. And keep your cat away from it:)