This is something else that could be in the Never give up category. (I recently posted about my 5 month fight to get a debit card, promised as a rebate.)
Camera is broken, so you'll have to put up with my little drawing.
One day, last summer, I found one of my in ground basjoos broken off, at just about ground level.
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The drawing, on the left, shows about what it looked like. The drawing, on the right, is looking at it from the bottom. The heavy black line, on the left, corresponds to the black shaded part, on the right.
The black part of the diagram was the part of the p-stem that was brown; not mushy, dut dark colored, like a banana fruit, or peel, left exposed to air. The light part, on the right, was cream colored.
What I deduced had happened was that an animal brushed against it, or the wind broke it off partially, (this cracked part sat for some time, and got dark) and then, at some later time, more wind, or another animal, finished the job. I picked the stem up, and cut it off at about 2 feet. There were no visible roots. (just about what is in the diagram) I dumped it in a 14 inch container, and let it sit. The center of the p-stem pushed out about an inch, and then stopped. A couple of months later (October) I moved it into the cellar, along with some other different plants. It still looked the same, with the center pushed out about an inch. The cellar is about 70° F, because the boiler is there. There are a few fluorescent shop lights there, the closest several feet from the plant. Everything got regular watering, about every 5 days, or so.
Now, 5 months later, I see a pup, with a 6" p-stem and 2 leaves, the largest about a foot (Total height about 18")