This looks like a pot of cylindrica leaf cuttings.

Sometimes these are sold, not even rooted.

If that is the case with this leaf, there is nothing much you can do. It will rot away

I think if you cut the top off, the remainder will pup. Providing the rot doesn't go all the way through it. All of those leaves should pup and not grow anymore.

They are all well rooted. They did well for a year, and I recently repotted. I just plopped it into a new pot, so the soil is same. I don't know why this happened. When I repotted, I noticed it had deep and crazy roots, more than my other varieties.

I would de-pot it and try to remove the old soil. If it doesn't come away easily, soak the root ball in cool/tepid water, it should be easier to remove after 10 minutes or so, don't leave it soak for hours. Get some better soil, at the very least use a good commercial cactus mix and add in extra perlite. I suspect that individual stalk is root compromised, leading to it not being able to drink up water, causing the shriveling. I would separate this one for the rest and pot it up separately. These are tough plants and should recover well from the rough handling.