There are several brands of thin epoxies made to penetrate rotten wood architectural elements that are too expensive to replace. You can drill a bunch of holes into the area, then with a syringe inject the slow setting epoxy until it won't take any more. When it sets, it will no longer absorb moisture needed to continue to decay.
When I work on some of the historic homes in my neighborhood, replacing column bases and post, I've started using this product ahead of the primer on even the new decay resistant wood like Spanish Cedar. My clients would rather pay a little more to not ever have to deal with these problems ever again.
Abatron is the brand one of my neighbors who does only restoration work uses.