We cut this plant, which was growing in soil outside our home in Los Angeles, at the stem a few inches above ground, just to put it in a vase for a few days thinking it would eventually die. It has been close to several months now and it just keeps growing with its base in water. Occasionally the bottom part of the stem will get brown and seemingly moldy, so we'll just cut that off and put it back into the vase and it keeps on going, with very light whispy strands (roots?) that look like tiny jellyfish tentacles out the bottom. In fact, it seems to have created a gel-like film around its base at the narrow opening of the vase to the point that when we tip the vase, water doesn't come out. I have taken several photos of the plant which is in the vase, and another photo of the same more mature plant that is still outside growing in soil. We're just fascinated.
SOLVED: Mystery plant that won\'t die
Cville_Gardener Clarksville, TN(Zone 6b) Mar 17, 2017
Kalanchoe delagoensis. http://davesgarden.com/guides/pf/showimage/245323/