You don't have to go to all that work, as far as burying fence etc, to keep critters from digging in. Actually the worst problem with the digging in are dogs. However, just laying the fencing down(we use 2X4" welded wire)on the ground(for keeping poulty safe)butted up against the sides of your pen will do the trick. Animals don't know to back up and dig..they will go right to the base of the pen and try and dig in. When we build pens here("we", meaning the Wildlife Homecare Network)for rehabbing we use 48" wire and place it on the ground with half in and half out as we are usually containing some of those predators that you are talking about.
Also, it's cougar that prefer deer for a diet. The Bobcat only measures about 24 inches long(discounting the tail)and the closely related Lynx is just a bit bigger. Normal diet for these cats is rabbits and hare along with small rodents, but as noted above they will eat just about anything they can to stay alive, even bats if they can catch them(this info is from stomach contents from hundreds of animals killed over a number of years). It behooves us to just take the simple precautions of protecting our birds(duhh, how hard is that, LOL)and not worry about it.
I live in a heavily forested area, on a river. and commonly see predator sign of most species found in the US(including bear, cougar, other wildcats, coyote, fox, raptors,you name it) and have never lost a duck to a predator. It's just not that hard to protect them. If we spent more time thinking ahead we'd not be out killing the animals that keep down the really dangerous creatures like mice, rats etc. LQ