That does look familiar, thanks for inviting my opinion. Here's Gibasis geniculata struggling in my basement in 2003 when I lived in OH. This is what it looked like by April. If you can keep it alive, it can get a haircut, repot, & grow back well once outside again. Don't worry about its' appearance for now as long as it's alive.
Your basement is probably coolish & fairly humid? In conditions like that, plants use very little water. If it's a hanging pot that doesn't have a hole in the bottom surface of the pot, it could be harboring about 1/2 inch of extra water. If you have a pruning nipper, you can snip a chunk out of the bottom of the pot, which will make sure excess water can drain out, though unless it becomes bone dry & weightless, I wouldn't water it while in a basement.
As insurance, you might try to find some stems that seem alive still and try some cuttings. If you have other potted plants upstairs, you could put cuttings in any pot that has some space at the soil surface. The existing root system of the companion plant would help your cuttings to not stay soggy while taking root, less likely to rot before they get going.
