Myself,...I wouldn't recommend putting down hardware cloth as the "floor" of the run. Like others have said,...a chicken's nature is to scratch, scratch, and scratch s'more.
We put down halved, heavy, "hog panels" as a two-foot apron surrounding my run, as our numerous coyotes are our greatest foes. Large packrats, and mousies a close second/third, for unwanted Varmints.
My run sits on a deep concrete sill, but this could be simulated by narrow concrete block, etc, as others have already suggested. I also place baited "rat-sized" HB Sherman traps near the coop & run (These are the best live trap, bar none, on Planet Earth). If you have robust roof rats, the traps that I use would probably be too small. The Sherman Traps that we use are 12" long x 3" wide x 3.75" tall. Baited with a wax-paper-peanut-butter-seed "bon bon".
My Aussie standing on unburied hog panel:

H.B. Sherman Live Trap:

We put down halved, heavy, "hog panels" as a two-foot apron surrounding my run, as our numerous coyotes are our greatest foes. Large packrats, and mousies a close second/third, for unwanted Varmints.
My run sits on a deep concrete sill, but this could be simulated by narrow concrete block, etc, as others have already suggested. I also place baited "rat-sized" HB Sherman traps near the coop & run (These are the best live trap, bar none, on Planet Earth). If you have robust roof rats, the traps that I use would probably be too small. The Sherman Traps that we use are 12" long x 3" wide x 3.75" tall. Baited with a wax-paper-peanut-butter-seed "bon bon".
My Aussie standing on unburied hog panel:
H.B. Sherman Live Trap: