I have had very few issues with rot where I live. When I have, you can smell it a few feet away! Yuk!
I dig it, wash off soil, cut off any sign of rot, soft spots, anything not normal. I put comet or some other dry cleanser with clorox or that says bleach in it (I have been using the same container for years) and let it sit out dry for a couple days. Then I re-plant and I don't water it very much.
When they regrow, they are never quite right. Lots of little fans come up from under the crown. Maybe 3 years later, I will dig that up and divide it and then you can actually get it going back normal again by dividing that mass of little fans into pieces.
I have to really love the plant to even mess with it. Usually, I dig it up and toss it.