Frayed cable at end of bar end shifter (on aerobar extension)

What Tim said is ideal (post a photo). I don’t have any familiarity with bar-end shifters — specifically how the cable is anchored to the shifting mechanism — but I probably would be inclined to just leave it if it was only a strand or two of cable that seems to have “broken off” there. The only thing to be careful of with electrical tape is the sticky residue that it leaves behind; again, not sure what this looks like, but if there is danger of the sticky stuff making contact with the cable where it enters the housing, this might interfere with smooth shifts (and persist as a problem even after you replace the cable). Again, I’m probably imagining this wrong

It does take a little while for the cable housing to compress (which gives the illusion of cables stretching), but I would still be nervous about replacing a cable *right* before an event. If you have the opportunity to spend a 2-3 hours on the bike beforehand, then you’d probably be just fine replacing it now and dialing it in on the bike. You may have to tweak the tension a little after a few weeks of riding, as Tim notes, but that should be relatively minor. (I suppose it depends on the housing you use; I use compressionless housing everywhere, so I don’t deal much with “cable-stretch” issues, but it still often takes me a few rides before everything is adjusted to my liking.)

Actually it’s not the cable that settles in. It’s the cable housing that settles in the ferrules. No need to settle the housing if you’re only replacing the cable. The housing’s already set. All you need to do is tweak the adjustment. IF you’re replacing cable’s and housing, cut the housing to desired length, make sure the curves are not too tight but not too long either. Thread the cable and secure it to the derailleur. Here’s where a sturdy stand comes into play. If the cables are NOT internal you can push down on the cables on the down tube by hand while you’re pedaling with the other hand. Give it a nice push for about 10 seconds or so. This action pushes the housing ends into the shifter body and the other ferrules. You might have to push more than twice to get a good seat. One you think it’s in there, tweak the derailleurs. I also do the same when replacing brake cables and housing. Good luck.

Replacing the inner cable avoids the settling that [as off2ride said] is due to the new outers snugging into the ferrules.
New inner cable, tune the deurallier, you should be good to go!
Alternative is ride with a couple of frayed strands, especially if they are not bothering you. Chances of the cable failing are slim. Feeling lucky?

@PotomacCyclist 62961 wrote:

You can see the strands on the bottom of the shifter in this photo. When the shifter is in the down position, it’s not a problem. When I pull back to shift to the big ring, then the strands get forced outward. That’s when I have to be careful not to hold onto the strands.

If the chance of the cable failing is slim, then I’ll probably wait on replacing it until after the race. But I will still need to put something over the frayed ends in the meantime. Those ends are very sharp. If I accidentally grab onto them (which could happen in the middle of a race), I could cut my fingers. (I’m not a fan of staph infections.) If I were going to replace the cable later on, residue from electrical tape shouldn’t be a problem. Or am I overlooking something? I’m not much for DIY bike repairs. I limit myself to chain cleaning, tire inflation, tire replacement and safety checks. If other work needs to be done, I let the bike store people take care of it.

I have bar end shifters on my bike as well, and have encountered this problem a few times with the cable fraying like this (although only with the cable to the rear derailleur, never the front. yet.) I don’t think the electricians tape will hold the broken wires back very well or for very long (as you say, the wire is pretty stiff). My attempt at a short term fix involved clipping off the ends sticking out with diagonals (wire cutters), which can work for awhile if you can cut them really close to where they begin to stick out. Of course, more of the wires will begin to break and then you’ll get sliced by them. (If you think about it, it’s an unstable situation: the fewer the remaining wires, the higher the tension on each of them– and they will start breaking sooner.) I would replace the cable as soon as possible and avoid the otherwise inevitable finger punctures.