Is it around a knot? If it's an old knot hole where a limb that died was, there will likely be rotten or pithy remnants of the old limb that can usually be pushed out or cleaned up and separated from the good wood rather easily. I've cut a decent amount of osage, but the trees I have access to are either so giant and tangled with other trees that they are far beyond my capabilities of safely felling, or they are younger trees 12"-14" max diameter. I've looked hard at the giant tangled trees I have access to, because there are several that have lots big limbs that would produce a ton of great staves...and these trees have wood that is deep, deep orange and drool worthy. While studying the trees trying to figure out how I might cut them, I've noticed that nearly all of them have large areas where big limbs used to be but have fallen or been knocked off. All of these area have significant rot like I described above, just much larger areas, and these rotted areas seem to extend deep into the center of the tree. The only living wood on a tree is the outter most ring of the trunk and limbs and the leaves and fruit, so if that inner, dead wood is exposed to the elements, it is going to start to decay to some degree. I'm pretty sure that the heart of these big trees I have access to are all rotted and hollowed out to some degree. You might have staves from a similar, older tree. That should not be a problem at all if you can remove the rot completely and still have nice, hard, orange or yellow, solid wood to surrounding the bow that you will carve from it.
