I didn't strip it. I found the wire exposed when I opened the case. I suspect that years of pulling the throttle to idle and stressing a wire that's almost too short has pulled off the insulation.
Oh, sorry for my English, I meant that I can't figure out a reason why the factory would have a bare wire inside a cable. As you said the wire seems almost too short, which can mean that the insulation hasn't actually pulled off, it has broken. If you opened the cable you might find out that the insulation continues at some point, probably quite close to where you've already shortened the cable cover.
After taking another look into your pictures and comparing them to a USB cable whose other end I have cut off, I came to think to another thing: USB needs four cables, Red, Green, White and Black. Yours has a second thicker black one, the one that's exposed. In my cable there's a braid covering the four wires as a shield for electromagnetic interference. The shield should be grounded to take effect. It looks like the thick black wire is connected to the shield, which is bare. Leaving it visible is not good craftmanship, but if there's no possibility for it to shortcut it's no big deal.
You can easily get a new cable, since all USB2 cables are basically similar. Only their quality varies. Simply get a good quality USB A to B cable like used for e.g. printers and cut the other end off, soldering the wires similarly to how they are now.