If the increases are far enough along, I would carefully cut/spoon the soft stuff out of the middle, then leave it exposed. Just to keep the rot from spreading further.
Had to cut the mother rhizomes off two new ones yesterday that have good increases. The mother was entirely soft but I was able to cut it off and gently lift it without breaking the outer skin. I poured bleach water on the cuts and they are now exposed to scab over. I really want to see both these iris survive.
