In looking at the photo, the wood looks to me to be "punky", no fibers anymore. Possibly because of it being soaked too long in acetone or whatever to remove the oil.
Also, from what I see, I don't believe that stock can be fixed well enough to shoot. That "punky" wood is soft now and unless the whole part of that stock is hollowed out and filled with some type of hard filler or better yet have it spliced with a good stock from that era.
As to the top tang broken, that steel was crystallized probably from being case hardened too long or not done right. Cases hardening should only be .003-.004 thousandths thick.

A question that has always bothered me, how do these stocks get that much oil in them? What do people do to get that much in them, especially in a side lock where the lock can be taken off and cleaned, then a Q-tip with a drop of oil will do one side.
I don't comprehend "oil soaked". The other is storing guns with the barrels down, ridiculous.
Barrles down only if you are short on space in the gun cabinet and have to put a gun in between.