Personally, I have rarely, if ever, had the rot spread to the increases. But usually the mother just shrivels. When I divide my iris, it depends on how much I like it and how well it increases. Here, it seems like the mother stays firm long after bloom and produces more babies. If I have plenty I go ahead and toss them, less dividing I will have to do later. A few just do not seem to multiply well and I leave the mother alone.