If this is due to so called 'dry rot', then the cause is the wood losing its seal against moistrue and small microbes (molds, yiests, etc) getting into the wood fiber and basically digesting it. Of course the other potential problem is termites. Those will eat furrows out of the boards that as you cut into it you will plainly see. The only fix here is to remove all wood showing signs of termite infestation and then treating your whole house.
However, assuming its 'dry rot', what you want to do is take a sharp knife or ice pick and come up from the ground, poking into the wood until that wood is solid. Then with a chistle or drill powered sharp round wood rasp, grind out all of the rotted wood until you have bright and shinning wood showing. If this area is less than 4" or so high and spread unevenly over the base of the door frame you should be able to repair it with epoxy. You can go to any good home improvement center and buy two part epoxy specifically for wood repair. Its kind of like mixing up Bondo for filling car dents. You then follow directions in mixing them and filling the wood voids. I always mix up a bit more than I need to ensure I have enough. Once mixed, It only stays workable for about 10 minutes or so, and you can start cutting/shaping it in about an hour, as I recall. Whats nice about using this stuff is that you can contour it and make it look like a continuation of existing molding. The epoxy is a little pricey, but its sure cheaper than replacing an entire wood column, wood pedistal, pilaster or door jam!