Re: slightly soft floor remedies
There are a lot of ways to patch it, but none of them are worth the effort. What you have is a section of plywood that has either rotted, or the glue has dissolved.
The right fix is just to replace it. Take the old piece and use it as a template for the new one. You are looking at maybe a few hundred dollars for the plywood, and an afternoon cutting it to shape, and then a few days varnishing. Compare this to any cheap fix, that might last a year or two, and then you are right back where you are now.