Thx again for your expertise pirate_girl. Ok, so this morning, I saw that my wee shoot (exactly as pictured above) had a rotten tip, even though the soil I put it in -- while I was learning what to do next -- was very dry. So I took it to a neighborhood plant master and got some pumice and more advice. So here's my current tactics: It's a hot sunny day here, so I'm drying out a pumice/potting soil mix on a baking tray in the sun. I trimmed off the tiny rotten tip and cut the rest of the shoot into thirds. Each of the new pieces has far more base surface area than the tip pictured in my original shoot. I'm keeping track of which way is "up" for these cuttings. I've made three small, high-drainage mini-pots out of plastic rubbermaid cups I had around. The drainage holes are for the future. I won't be watering them for quite some time. I intend to put the three shoot cuttings into the dried-out pumice/potting mix and leave them be. I sure hope the sun-baking and increased root surface area is enough to prevent rot. I don't know what else I could do to prevent rot. So that's my plan for now. Any comments are welcome and appreciated.

Pictures would help. Also keep dry. Sounds like water did the damage already. May be too late. What type is it?

Sansevierias are pretty much damn near indestructible. Provided that they're not overwatered. These plants prefer a fast draining mix that doesn't stay soggy, such as a cacti & succulent potting mix. When you do pot it up, don't pack the soil down around them. What I like to do is fill in the soil and then hit the sides of the pot to settle it down as far as it can on its own. This lets the water flow freely, as well as letting your plant's roots breathe. When it comes to watering these plants, less is most definitely more. And by that, I mean infrequent watering, not how much water you use when watering. I always flush out the entire pot, making sure there are no hidden pockets of dry soil. Truthfully, I leave mine outside and just let the thunderstorms water them for me. I rarely, if ever, water them when they're outdoors. And when I do bring them indoors for the winter, I rarely water them even then. To give you an example, These leaves came from one of my solid green Sans. They have been sitting on a shelf without any soil or water from since the beginning of the year. The only thing they've received is bright, indirect sunlight coming thru the nearby window. As you can see, they look just like they did when they were taken off of my other plant. These plants are tough, and can withstand quite a bit of neglect. Now that I'm thinking about them, I'll finally get them potted up, haha.

Mushy at the bottom is an indicator of rot, sorry, but that doesn't bode well for the plant. The remedy for this is to correct your soil, so it doesn't stay so wet. One needs to be able to water the plant well, little sips are not the answer. If mine, I'd unpot the whole thing & check the roots for rot. Then I'd repot in more appropriate soil & leave it be. You could try growing that root to see what happens.