We live in the sticks and have a coop that can be moved around our grounds which we do frequently in in the summer. But we live in the Northeast so it is stationary over the winter and they lived on the dirt from November til Spring. We haven't had any problems with animals digging to get in. However, we bring in the chicken feed at night so there is less temptation for nocturnal animals to want to get in. It is easy enough to take them their food in the morning when we let them out. I have seen squirrels, possums, and other animals near the coop but nobody seems to be interested in getting inside when there isn't food available. We have a tiny flock of four so I can only speak for our situation.
We have thought about getting a more permanent run with gravel or other bedding on the ground but they love the fresh grass so we are going to continue to move them about the yard when we can without the protective foot of underground hardware cloth. We feel that so long as they are safe in the roost at night we are comfortable without added protection.
HTH,
Katalina