I would did the cloth down atleast 6 inches, but I would also skirt the outside of the run. What I did was dig the hardware cloth 12 inches below grade and then bent it out in an "L" shape and then covered with dirt. Haven't had any problems and I've got raccoons and possums around. They'll get frustrated with the wire and usually stop digging. Covering the bottom of the is a good idea too. I ended up retro-fitting my run and it was sort of a pain, but I sleep much better at night. You can never be too protected, in my opinion. Good Luck and so sorry about your losses.
Emily
Emily