I cut them off, making sure anything that looks rotten is removed. Less bruising of the plant that way.
Marylin has it exactly right. Wet semps in our direct sun will rot at the roots and base. Then, without the ability to get water to the tops, they just shrivel up in our very low humidity. Now, they need to callous over at the base and then grow new roots.
Once replanted, do NOT put them in direct sun for quite a while yet. At least not for several weeks, maybe longer, until they are well rooted again. Otherwise they will just shrivel. Maybe no mid day sun for the rest of the year. I try and keep all my potted semps out of the mid day sun and new ones out of all but early morning and late afternoon sun. Ever feel the dirt in those pots that are in full sun at noon? It's not just warm, it's hot! Put the same pot in the shade and it feels cool.
I just bought a semp at a nursery that was headed this way. The top still looked great, but I could lift the entire clump off the pot because all the roots and base had rotted. Given time, the top would start to shrivel but it hadn't got there yet. Too many nursery staff overhead water the semps in the middle of the day, so this is very common. I'll just reroot it.
