Though most Begonias do great at my house, my only experience with a tuberous one was this past spring. I was told it wouldn't like the heat here, and sure enough, after a few really hot days, it melted, for lack of a better word again. The stems fell over and the ends looked like the one in the top circle. Aside from that 'puckered' stem end, your pillow misadventure and this story have nothing in common (and I hope it stays that way!) The middle one looks great!
The end I circled at the top looks like it had separated from the rest of the plant already, puckered shut, for lack of any more proper terminology to throw out there. The one nearer the bottom just looks dark, like maybe in the process of puckering shut. I hope I'm totally wrong, and should have been more specific in the first place. Sorry, they're replacing our roof today and it's noisy!!