They can certainly dig deeper than 6-8" -- but even moreso, so can *predators*. I'd really suggest a better digproofing arrangement; not so much to keep hens in as to keep dogs etc *out*. Either dig in some (heavier gauge) wire mesh deeper than you've got, or lay some on or just under the ground *outside* the run for 2' or so to the outside of the run fence (attached to the bottom of the run fence), well weighted or pinned down or covered with turf.
If you go the apron-outside-the-run-fence route, you still may have to repair occasional dusting holes that drift partly below the fence (jsut to avoid tempting predators) but nothing bad can actually come of their doing that.
If necessary you can also put a row of bricks, good-sized rocks, small pavers, etc on the ground along the inside of the run fence, so that their dusting holes don't get so close to the fence.
As others have said, making a *good, appealing* dusting area elsewhere may also help, although it may require experimentation to get it so they like it. Also if your run is pretty small (8 sq ft or less per chicken) expanding it would help a lot.
Good luck, have fun,
Pat