A good set of headphones can last a lifetime, but it's unlikely that the plug at the end of the headphone cord will. If you can solder a wire, though, there's no reason you can't replace it. If you don't know how to solder, you can buy a replacement plug that uses screw-on terminals, although this will be less secure over the long run.
Use wire cutters/strippers to snip the old headphone plug off the cord. Purchase an exact replacement headphone plug at an electronics store.
Twist off the shell of the replacement plug and slide it and any insulating sleeve onto the headphone cord.
Using the wire cutters/strippers, remove 1 1/2 inches (4 cm) of the outer insulation from the headphone cord. You should find three wires: two insulated wires and one uninsulated wire, which is the ground.
Strip 1/2 inch (12 mm) of insulation from each of the insulated wires (see A).
Solder or screw the uninsulated ground wire to the plug terminal that is farthest from the plug tip (see B).
Solder the insulated wires to the other plug terminals. If you don't know which terminal on the plug is the right channel and which is the left, you can use a continuity tester (available at electronics or hardware stores) to find out, testing it first on the tip of the headphone jack, which is always the left channel.
Squeeze the plug clips together with a pair of pliers to secure the cord.
Slide the shell over the plug and screw the plug in place.
Things You'll Need
Soldering Iron And Solder (available At Hardware Stores)
The wires for Sony headphone cords are insulated with a lacquer coating, which you'll need to remove before soldering them to the new plug. The easiest way to do this is to gently scrape it off with a pocketknife.