Frayed cables are often simple to fix; you just twirl the end between your fingers to rewind it, then pick out any out of place strands with your fingernails and push them into place as you twirl the cable. Unwind any bent strands a few turns and cut them off before the bend (you can't easily bend them right again), and rewind them.

To get the end of a cable through any resistance? Twirl it, baby