C/A is not your only solution. A product called "Clear Penetrating Epoxy
Sealer," made by Smith and Company, Richmond, CA, and sold in a number of
woodcraft type stores may do what you want. I have used it for repair work,
and have seen it used for turning punky and decayed wood. It locks the
pithy fibers together so they keep their shape when they are turned. I used
it to re-anchor lag bolts that hold my porch rail to the house. The
"carpenter" who installed then didn't use any sealer, and rain water
eventually caused so much decay that the lag bolts started to pull loose.
It's solid as a rock now.