This is a great mod to try if you want to enhance cheap earbuds/earphones or your cord is already broken somewhere (hopefully at the plug end, because it's usually difficult to figure out how to take apart the in-ear units if no one has already documented the procedure).
Essentially, to proceed with this mod involves re-making the Y-junction where the common cord splits left and right. Having to cut and rejoin wires possibly degrades audio quality¹. It's likely that you'll notice one of the binaural output signals being noticeably weaker, especially as you lower the volume on your audio source, but this condition is common on cheap headsets to start, so this is why I do not recommend you try this on expensive gear and fail to like the results.
However, it's possible to not introduce more points of electrical resistance, by choosing to redo the existing solder points at either end, if you willing to perform a more laborious rebuild.
As another caveat, depending on how discriminating you are about your listening experience with in-ear headsets, this mod might not be worth it. Paracord, being made of rigid nylon, will audibly and crisply chafe (therefore transferring this sound to your ears), but the use of a clip should reduce this by keeping it from sliding against the sides of your face and any hard fabric you may be wearing.
See the last step of this ible for more notes.
Step 1: Gather Materials
• Paracord of your choice. I assume the larger the diameter the less prone it is to flexing and therefore tangles/knots, but there isn't any significant diameter variety.
• Sacrificial earphones or earbuds with a cord thin enough to be easily thread through the outer jacket of paracord. The ones used here are Sennheiser CX55 In-Ear Headphones.
• Heat Shrink Tubing of various diameters
• Electrical Tape; depending on your earphone design you may have to tape the ends so that the heatshrink tube does its job of holding onto something with the paracord in place.
EDIT: Actually, super glue is more effective than tape. After a few months tape will tend to fail. I guess some sort of plastic cement might work, too.
• Small alligator clip (optional). I recommend clipping the cord to a shirt so that the headset remains in the ears and the cords freely contacting only air, despite whatever odd looks you may get from onlookers.
• scissors or knife
• wire cutters/strippers
• lighter (preferably a butane, torch type)
• soldering iron, flux, solder