I've had my lucky bamboo for about 9 months. I got it from a mall store which seemed to take care of its bamboo really well. When I got the plants home, both stalks were fine for a very long time. But, only one has actually grown. The other has a brownish-black spot near the roots. It doesn't include all of the bottom, but just that isolated section. It's just enough to keep the plant alive, but it doesn't allow it to grow. I was wondering if I should cut that dead part away, or if I should leave it. It's been like this for the last few months, and hasn't affected the plant otherwise or spread.
It could be damaged or rotting. Or it could be fine. No way to tell from the description. Take a knife and scrape at the spot. If it is soft you can cut it out, but you might have to cut the whole bottom off above the rot and stick the top into the water so it can grow some new roots. Or you can leave it and wait.
It is not actually a bamboo at all. It is Dracaena sanderiana and there are many threads on this forum as to the disadvantages of growing them in water... Ed