Thanks for more responses.
Yes, there are bobcats in this area. I did see a large cat (larger than a housecat) crossing the field one day. It was carrying a rodent. It didn't look like a bobcat, though. It was dark and had a long tail.
The fence has been repaired, then broken (bad extension cord), then repaired, then broken (ground wire completely severed), then repaired. Currently it's largely coated with ice, but charging nicely where the ice is broken off. The ice splinters off when anything knocks against it, so hopefully a predator would get a shock.
The trail cam has caught mostly rabbits, but I've seen two coyotes, and possibly a raccoon, all outside the fence. None approached the fence; they all skirted it. There was one opossum inside the fence. I had traps set for it, but I can't seem to catch it.
I thought I had the problem licked, then I found another half-eaten pullet yesterday. I'm frustrated enough I stopped at the gun counter at
Walmart to ask advice this evening. The lady at the counter happened to be a chicken owner who'd lost quite a few birds recently herself. She advised me to bait the trap with the half-eaten bird which I did tonight. Makes sense. Maybe I'll catch him tonight.
A couple of nights ago I saw a pair of eyes glowing from a tree hanging over the barn. I was able to get a pretty good look at it. It didn't look like an animal I'd seen before. I guessed maybe badger, but a facebook friend said he thought it was more likely a opossum. I didn't realize they could climb so well. Anyway, it didn't look like a opossum to me, and I've see quite a few of those, but maybe it was.