I know I am late to this thread, but what you describe isn't a snake. Snakes don't usually venture far from what ever they have struck, even if the strike was in self-defense. Unless a copperhead (or any pit viper) is really hungry they don't venture out in the open except to sun and they really prefer to avoid humans or critters they can't consume. While they will eat eggs they still won't venture very far away once they consume the egg and still prefer that egg not be associated with human scents. Before any of you tell me about Black Snakes and such they are not pit vipers and unlike their poisonous cousins have to take when the taking is good. I'd rather lose an occasional egg to a snake if it keeps the mice, rats, voles and moles at bay. There is a 6' black snake that free ranges the wall and floor spaces of my home and I haven't seen a mouse in two years. Now if you really want to rid yourself of snakes you don't need to be St. Patrick or have a mongoose. Any member of the Goose family (yep the bird) will keep your coops safe from snakes. Geese will attack a snake, in a heartbeat, including pit vipers. Remember those cats you keep running off. They are snake killers too. Watching a cat take out a pit viper is rather entertaining, unless you are said pit viper

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From the symptom you described I be looking for Fiddler Spiders (Brown Recluse, Wood), or Sac Spiders. The venom of these spiders are hemotoxins and cause blood vessels to constrict, which in turn causes large scale necrosis. Bites on mammals and avians are self-defense bites, but still bad. Humans have been known to lose limbs or die from a Fiddler bite if not treated properly. Any bite to critter the size of a chicken could easily kill and it would appear to be instantaneous even though the bite occurred 48-72 hours prior. I have seen similar reactions of dogs I have breed.
I know chickens will eat things that crawl, but they aren't immune to the spiders bite. Other than keeping these spiders away from the coop there's not much you can do if a bird is bitten and you will definitely not see where it was bitten.
Sorry for the diatribe