The term you are looking for is called the Hill Sphere This is the area where a body can orbit and not be perturbed out of said orbit, assuming two gravitational sources and no external factors. The Hill Sphere for the moon, for example. is roughly 35,000 miles. Anything small in that space SHOULD orbit the moon in a stable state for long periods of geologic time. Then you have to factor in the pull of the sun, the push of the solar wind, Jupiter's gravity, Venus etc. And, oh yea the lunar gravity field is 'lumpy' and not smooth; satellites in orbit at low altitude will become unstable quickly. Realistically anything over 200 miles and under 10K miles should be stable over long time frames. That there is nothing there tells us that the sun et. al. helped clean this area of space.
Saturn has two moons, Rhea and Iapetus, with equatorial ridges that for all we know about how space works looks like a moon had a slow impact, or that body hit the Roche Limit and became a ring that then spiraled into the moon and left its ridge.
Articles have been written about what this would look like, but none have been found. In short, gravity is complex, and other factors work against moons having stable orbiting bodies around them.