Well, mine has dead stems all the time too and spreads really good. I was told to cut one of the live stems and put it upside down in water to grow another one. Ever hear of that? The tops of mine never hang down, they always stick up! That's why I wasn't sure what it was.
Yes, it makes new plants on the ends of the stems, right in the middle of the leaves. Turn a stem upsidedown and stick it in the water. Sometimes they will make baby plants even out of the water.
This plant does very well actually growing in water as a bog plant. If it dries out too much will quickly turn brown. This is easy to grow from seed too. Park Seed used to carry them under the houseplant section.
I have one! It does root verrry easily in water...before you do this though...cut off the outer portions of the leaves, leaving just a small(ish) circle of leaf 'portions' around the stem...that's the recommended way and it helps, as those leaf portions you cut away don't just 'rot' in the water. The stems of mine flop over once in awhile too, if they get 'bumped'...they're kindof fragile...it does grow like a weed and definitely can't be overwatered!!
I received mine from Connie and it is the same as I got in a trade from tiG. Now I have twin umbrella plants to go on each side of the pond. I have named them Connie and Bonnie. Isn't that great. I couldn't have planned it any better. Thanks girls and hope you don't mind the naming. Jim