Well, the fast answer is "yes. trim of the old soft, (or rotten)parts of the rhizome. Then, I would dip the rhizome end (and about the bottom 4" of leaf) into a solution of 1 cup household bleach, and 9 cups of water....let them soak for about 2 minutes....shake 'em off. let them dry, and then replant. Ideally, the BEST time to dig, divide, and re plant is about 2-3 weeks AFTER they bloom....this gives them plenty of time to root in, and grow new increases before winter, so they are "ready to go", when spring arrives. Spring division will REALLY cut into the bloom this year....but, in some cases, it IS needed! I'm having to dig ,and treat a lot of mine now, because of disease.
It is "normal" for the old, spent part of the rhizomes to dry, get hollow and sometimes sort of 'soft and mushy'....the mother rhizome blooms just once, and soon after, starts to "die"....by this time the newer "daughter" rhizomes (the increases that started last year) have grown to a size where they will become "mothers " themselves...blooming, producing increase, and then, in turn, dying themselves. There are several "articles" on digging and dividing" as well as on diseases (to help you see if the "rot" you are seeing is the natural decay of a spent mother rhizome, or if it's a serious disease.
