The transom is more than likely rotted. Water has gotten into the transom which is a Balsa cored. When water saturates Balsa long enough it turns into a wet paper bag like material.
More than likely water ingression is a result of a failure of the caulk sealing the transom assembly.
To fix it, you'd basically need to remove the engine, cut out the inner skin of the transom in the engine compartment. Then hog out the bad wood. Insert a new sheet of marine plywood epoxy it in, cover it with many layers of fiberglass, then seal it with something like vinylester.
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