Back to your first question, do you have to have a run? Can you possibly build one that will keep every potential critter out?
You do not absolutely have to have a run. Some people don’t but just free range. A run adds tremendous flexibility to you. There are times I want to lock the chickens up and not let them range. Sometimes this can go on a week or more, say a hen is hiding a nest and I want to retrain her to use the nests in the coop. My run is split in two, with the main coop on one end, the grow-out coop on the other, and a gate in between. That comes in real handy when I’m integrating. There are lots of other reasons a run comes in real handy.
The larger the run the harder and more expensive it is to make it to make it totally predator proof. I don’t think you can reasonably build anything to keep mice out; snakes and weasels are really hard. But you can build something that will keep the vast majority of larger critters out. A high fence will keep coyotes, dogs, and other critters out. If you put a top on it you can keep flying and climbing critters out, but the bigger it is the more challenging that can be. You need to support a roof, even if it is wire, against snow and ice load too.
I use the philosophy that I have a mostly predator proof coop where I lock them up safely at night. My run is predator resistant. It will stop anything that can’t climb or fly except maybe a bear and those are pretty rare here. A climbing or flying critter could get in but they haven’t yet. I also have an area inside electric netting that has stopped any non-flying critter. The electric netting is not much use in snow. If the snow is wet it will ground it out. If it is a really dry snow it will insulate the critter from the ground so the circuit is not complete. If you go with electric wire (not netting) you might want to run a ground wire for winter.
A decent run adds a huge layer of protection. It may not stop every imaginable threat but it can stop the vast majority of them. In spite of what a lot of people think, just about anything that eats chicken will hunt during the day. But most are more active at night plus there is a lot less human activity at night. They have more undisturbed time to wreak their havoc.
Instead of burying wire to stop digging predators you might think of using an apron. You take a piece of fencing maybe 18” wide and lay that horizontally around the outside of your run and coop if appropriate. Attach that to the bottom of your run so nothing can squeeze through. I use J-Clips but hog rings or just weaving a wire through it will work if it is wire. If you have something at the bottom to screw to then you have other options. You don’t have to bury it, just hold it down for the grass to grow through it and hold it down. A lot of people remove about 2”, which is the turf, and put that on top to help keep it away from lawn mowers and weed eaters. The idea is that a critter goes up to the fence, starts digging, hits the wire, and does not know to back up. You need something at the bottom, especially if it is wire. You will find it almost impossible to stretch wire and not leave gaps. A possum, skunk, or raccoon needs just a tiny gap to be able to squeeze through without even digging.
One trick I used to help reduce the chance of a climbing critter getting in. I used five feet high 2”x4” welded wire for my basic run, covered part of it with a metal roof high enough I can walk under it without hitting my head, and filled in that gap with more wire. On the part that is not covered I took more of that 5’ high wire and attached it to the top of the fencing, overlapping about two feet. The wire is stiff enough to stand on its own, so the fencing winds up about 8’ high. But it is flexible enough that if a raccoon, fox, bobcat, or something else tries to climb it the wire will bend over backwards so the critter has real problems getting over the top. It’s not perfect, corners and such are a problem, but this adds an even greater layer of protection.
You might think of a run as similar to driving to the grocery store. It’s possible a critter can get into a run. It’s possible you can have a fender bender driving to the grocery store. Safe driving habits can keep the odds of having accident really low and the severity of that accident lower if it does occur. The better your run the less likely a dangerous critter gets in. I’m not afraid of driving to the grocery store because an accident could possibly happen but I take what I consider reasonable precautions when driving. Just because a critter might possibly get in does not mean one will, especially if you take reasonable precautions.
I think the wire apron and letting the grass grow through sounds like a terrific idea. we'll have to see exactly how big our run is, before we decide what we'll do with the top, but the bendy wire idea is pretty ingenious if our run is large for other types of mesh.
