Well, if you are truly on solid ledge, if you think about it, although YOU can't dig thru solid rock, neither can predators
However IME the situation is seldom that simple (and when it is, it's actually quite complex in other ways, i.e. b/c you can't sink posts and the run thus needs to be strongnly anchored in some other way, which can be a giant PITA).
In reality, your best solution is likely to do a wire apron along the outside of the run, at least 2-3' wide, securely affixed to the foot of the run fence, with the edge turned down a bit so's not to be obvious, and either pegged or weighted down real well all over, or covered in whatever material you choose (turf, mulch, rocks, concrete rubble, whatever).
This is usually the best solution for MOST people IMHO, because it is ever so much easier and works just about as well as burial (which really needs to be 18" deep if you want reasonable peace of mind... and boy is that a lot of work even in light sandy soil...).
Good luck, have fun,
Pat