If you know more rain is coming, best to pick them now, leave in pods, string on thread like popcorn chains, and hang in a warm dry room in the sun with a fan on them. If you shell them, you can spread on an old window screen laid flat with a fan on them.

The fan is the important part. I didn't have enough room under the fan so put some of my pods on cardboard on the dash of my car. They stayed damp and molded, while the ones under the fans dried quickly.

Ditto on picking quickly, leaving them in the pods, and on the fan recommendation. Damp beans spoil or rot very quickly. Rain (during the period that pods are drying) costs me a large part of my dry bean harvest most years. Fortunately, due to a well-timed dry spell this year, it was not much of a problem for me.

Whether or not the beans will still be good - even after drying - depends in large part, I believe, upon the hull protection afforded by the variety. Some varieties that I have grown have been good even after extended periods of rainfall... but they are the exception. Those varieties mostly had pods that shrank tightly over the seeds as they dried.

I wonder though; were the pods exposed to frost? Don't know your location, Kay, but your zone makes me wonder. Much of the North has already had a killing freeze, and frozen pods can have the "terribly soggy" appearance you describe. If that was the case for your beans, open a few pods & inspect the beans. If you find discoloration or shriveling - or if there is already excessive decay - then the beans were probably frozen. In most cases, this would kill the majority of the seed... so it might not be worth saving, unless it is irreplaceable.