If I have a tuber that is rotting from the root end, I cut off the rotten part, and then plant the tuber in a pot HEAD DOWN in moist potting soil. I bury the tuber on a slant, with the head well under the soil, and leave the cut end sticking out the top. The cut end usually dries and does not rot much further. The tuber can be a food source for the shoots even if it doesn't have roots of its own. Usually the new shoots grow roots of their own reasonably quickly, which is what they are supposed to do anyway. The mother tuber can be cut off after the shoot is growing well, but I usually don't bother. I have even had success with a few where the rot was down one side, or the center of the tuber but hadn't reached the head yet. I had to water the pot carefully, to avoid getting any water into the hollowed-out tuber, but mostly it worked.
