From your description it sounds like an area of rot centered around the transmission below......but you would know in short order if that was leaking oil and throwing it up on the under floor space (Ujoint rotation with a rear seal TX leak) I am sure.
Water does move around in secretive ways, but to rot the floor it would have to seep under the lino/floor covering from somewhere.....or as stated by others, from road wash underneath. Maybe you have other soft floor area caused by a kitchen tap/drain/hose leak, but it might be under cupboards or other living space items where it is not so obvious? How would it collect and rot the area you can feel is soft, is the question? Perhaps also check under the large slide and make sure the sweep is in good condition and the flooring when slide is out is solid. It will be interesting to hear what you find.