What should I do about old cables that have been damaged?
Repair

You can use a cable jacket repair tape, to repair the jacket. I would not use simple electrical tape to make the repair, since it has a tendency to dry out and fall off.

Scotch® Cable Jacket Repair Tape 2234




  Repairing Damaged Cable Jacket When No Portion of Cable Jacket is Missing
  
  
  Abrade the cable jacket 3" (75 mm) beyond each side of the damaged cable jacket section
  
  Wrap one half-lapped layer of Scotch® Cable Jacket Repair Tape 2234 extending at least 2" (50 mm) on each side beyond the damaged cable jacket
  
  Starting 1" (25 mm) past the Scotch® Cable Jacket Repair Tape 2234, apply 3 half-lapped layers of Scotch™ Super 33+™ Vinyl Electrical Tape to each end to temporarily secure the ends of the Scotch® 2234 tape to the cable jacket until the tape reaches full bond.
  
  
  
  Instructions


NOTE: Other products do exist.  The products listed above are for example purposes only. I do not recommend or endorse the above listed products.

Replace

If the section is accessible at both ends, you could simply replace the section of cable.