Looks like Mealies feeding on the rotting tissue. Sans are strong plants that mealies can't hurt but with some thing else happening it can be deadly. Looks like over watering. I bet most of the roots are rotted also. I would pull it out of it's dirt and plant in pure perlite for now. It also needs a wash to stop the mealies. I would use some thing like Bayer 3 in one spray for roses. If it recovers, 50-50 at this point. They you can replant it in a cactus mix with extra perlite. Best of luck with this one. Let us know what happens. We are all still learning here and it can help all of us out.
Remember mealies are quick spreaders so keep it away from your collection. Some just toss the plant rather than risk the chance of loosing more costlier plants.
Stush

Stush, thank you for your reply. Here is a photo of the whole plant, so as you can now see, it is only a small part affected. No mealies - what you were seeing was perelite left on the leaves after a recent repotting. The roots appeared healthy. I should have mentioned, the growing tip in question on this plant seemed unable to open on it's own, so when I "helped" it, I found the brown inside. I'm wondering what would happen if I took an exacto knife and just cut that whole tip out? I might ruin the shape, or maybe it would produce more pups? I don't guess I have much to lose if I try.....

Most likely you will damage it and it may do just what you stated. Still not bad. Plant looks better as a whole. With warmer temps. you can put outside is part sun and let nature take care of it.
B.T.W. Doesn't look like a tipical S. trifasciata. Could it be S. 'Senegambica' ?
Stush

I just read on another Forum about T8 lights causing burn damage on some plants....I wonder if that's what I could have here? My plants are all under T8s most of the year and generally do well. And no, it's not a typical trifasciata...I think it is S. 'Okeechobee', but can't find enough information to be certain. It came from a greenhouse that sells unusual succulents.

I keep most of my collection under T-8's all winter long. I didn't have trouble this year with them or the few I had last year. Mine are on over 12 hrs./day. Any link to the other artical you found?
Stush