My cat recently chewed through a fair amount of my beloved Korean Vibe BS-80HD ear buds. I had several options, I could:

Buy a new pair for like fifty bucks
Repair them and use some fairly ugly heatshrink smack dab in the middle of the cable
Go all out like in this instructable!

Covering your earbud/headphone cables with material only requires basic soldering skills and patience!

Step 1: Materials/Tools

Materials
Earbuds to be covered
72" of round shoestring (if you order 72" shoestrings you will have double the amount, as there are 2 shoestrings)
3.5mm (1/8") gold plated stereo audio jack with built in strain relief (obtained at radioshack)
6mm Cable Pants
6mm Heatshrink (I used black)
A little bit of epoxy
Tape
Some solid-core wire (such as 24 gauge or something like that)

Tools:
Scissors
Wire-strippers
tweezers (optional)
lighter (good for melting ends of shoestrings and shrinking heatshrink)

Note: If you are doing this mod to headphones who's cable doesn't split to the left and right ear (such as beats headphones), you do not need the cable pants.

Step 2: Butcher the Ear Buds

This part is kind of tough (snipping a good pair of earbuds!). You have to snip the ear buds in 3 places:right above and below the splitter, and right above the 3.5mm jack.

If you are doing this to headphones with a cable that doesn't split, you only need to snip off the 3.5mm jack.

Step 3: Preparing the Shoestring

To prepare the shoestring, simply cut off the plastic ends and pull out the core. Singeing the ends with a lighter will prevent the chord's edges from fraying.

Once the core is removed, feed the entire shoestring onto a piece of solid core wire. This makes it much much easier to feed the shoestring onto the flexible cable used in earbuds/headphones.

Step 4: Transfering the Shoestring

To cover the original cables with the shoestring,it's easiest to tape together the audio cable with the solid core wire as shown in the picture. Now that they are taped together it's easy to move the shoestring over, inchworm fashion.

Cover the cable that connects to the 3.5mm jack first. Cut off the excess. Make sure you pull the shoestring taught when cutting so that stuff doesn't bunch up later. It's actually better to make the shoestring a tiny bit shorter than the cable to allow room for soldering later.

Step 5: Soldering the 3.5mm Jack

Self explanatory:
1) clamp the shoestring/cable to the connector
2) Solder gold to ground, red to right, and blue to left
3) Slide the other pieces in the order of the picture. You may need to tape and cut the other end of the shoelace so you can slide the pieces on.

Step 6: Coat the Earbud Cables

Slide the shoestring onto the cable connected to each bud in the same way as in step 4. Then cut 2 short pieces of heatshrink and place them right next to the bud as seen in the picture. This piece of heatshrink elegantly terminates the shoestring and keeps the shoestring from moving around on top of the cable.

Step 7: Preparing the Cable Pants

The cable pants provide a nice way of splitting up the cable to the two earbuds. The cable pants come with a lot of extra plastic, so just cut off the excess with scissors.

Step 8: Slide the Earbud Cables Into the Cable Pants

This is the hardest part, it's really hard to fit the cables into the cable pants. One way of slipping the cable into the cable pants is by feeding a wire through the pants and then taping the wire to the cable . Once they are taped together you can pull the wire into the pants.

Do this with both earbuds and slide the pants up so that there is no chance that the pants could fall off.

This step by far takes the longest (took me an hour and a half once).

Step 9: Joining the Cables

This part is pretty straight forward, just strip and solder! Gold goes to gold goes to gold, red goes to red, and blue goes to blue.

After soldering, apply some epoxy to the joint for electrical isolation and mechanical strength.

NOTE: Do NOT go overboard with the epoxy otherwise you will not be able to stuff the joint into the cable pants.

Step 10: Slide the Pants

Once the epoxy is fairly cured (but still a little sticky, so like after 5 minutes), slide the pants over the joint. The epoxy will hold it there and it looks professional.

You're done!