I don't know what kind of begonia this is, but I just got it a month ago. Hadn't been keeping up with watering, and as a result, some leaves dried up and fell off. And eventually one of the two stems turned black from the bottom and completely died, and then the other one started turning a darker green and getting wrinkly and kinda mushy. So apparently rot.
So I cut it, and the inside of the kinda-mushy parts is still light green? Usually rot has a discoloration.
I'll get pictures of it after being cut, whenever I find where the heck I put my camera.