Black walnut makes an alopathic chemical called juglone to inhibit other trees from growing too near to it. Juglone in soil is peristant and can kill tomato. The sooner your BW stump is well and truely dead, the sooner other food can be grown proximate to the old stump.
That probably explains why some things will not grow near the stump... Weeds dont give a darn. I have other black walnut trees on my property, and there are all kinds of things growing under and around them. Irises thrive under them, as do peonies, Dame's Rockets, and others. Spinach, lettuce, blueberries and raspberries do not grow there. Perhaps the potatoes also do not like it? [I thought they drowned in the flooding we have had.] I have some weed killer that kills roots, though I do not like using the stuff. I got it to kill poison ivy as I am very allergic. That might help to kill it off ? maybe ? The elm tree next to is also trying to come back. Rose of sharon bushes have no objections to the black walnut either.
I am sure you could google for a list of plants that will or will not grow near a black walnut tree. Usually it is a list of plants that won't grow there. (Azaleas, Rhododendrons, pampas grass etc.) IF there are still roots that are sprouting, which I don't normally see that occur with the walnuts, do spray them if you want. You could always use a propane torch on them, to scorch the growth, and that should fix them also. You still will not be able to grow things there as the juglone will still be in the soil emitting its noxiousness for some time.
