Curse the Gods, and unwrap the visible wire ends until you go through the damaged layer and can use the remaining good one.
No magic bullet here, just use good light plus a magnifier or stacked reading glasses.
You won´t be so lucky as to pick ends in proper order, so unwind as much as possible, under light thension (or it will stick), as soon as you feel resistance you pick another end and so on.
And ... good luck
Plus LOTS of patience.