My understanding from what I've gleaned from different threads is that stumps randomly and slowly accumulate objects. The contents of a stump is independent of whether you look at it. Most stumps have nothing in them, but if you find an area that is especially depleted in stump-findings, it's possible a previous forager cleaned them out.
I know that near my base, I've cleaned out all the stumps, but then one time when I looked again in a stump I was 99% certain I'd looked in it before, I found a WORM.

I think I also read that you can create your very own stump-farm by planting a bunch of trees and cutting them down but leaving the stumps behind.