If it's shorted, replace it or cut out the shorted section and make a splice. If it's open, replace it, repair the broken section, or cut out the broken section and make a splice.
It's possible to repair many kinds of damage to wires, but your question is essentially equivalent to "My head hurts, can I make it stop hurting?" Sure, if your head hurts because of sinus problems, a pill can take care of that. But if you have a nail embedded in your skull, that requires a rather different solution.
Headphone cables, for instance, are generally replaceable (with a bit of doing, unless the 'phones are actually built to be taken apart) but not generally repairable. Cat5 cables are easily replaceable but repairable only in the sense you can cut off one end and then crimp on a new connector.
tl;dr: It depends.