There's got to be a hole in there somewhere; it definitely sounds like a weasel, mink, or stoat if there's injury to the neck. They can climb through holes that are 1/4" - I know, because I lost five ducks in one night to one. After checking the duck's coop, we were able to determine where entry was made based on the claw marks, and no kidding the hole was that small. They were climbing up the side of it and dropping in underneath the roof. We fixed the problem, then my husband and I sat out for hours until we finally caught them red handed, and the attack was during the day. In our case, it was a "herd" of five stoats. One way to check for the entry point is to go in your coop at night with a flashlight while someone stands outside to look where the light is spilling out. You can try setting traps, but the problem with that is you kill one predator and another moves in to claim its territory. Your time is much better spent making the coop area impenetrable.
I had to look that one up, 'cause I'd never heard of the stoat (Mustela erminea), also known as the ermine or short-tailed weasel, is a species of Mustelidae native to Eurasia and North America, distinguished from ...
I say kill 'em: Kill 'em all AND secure your birds more completely.
My little brother reminded me of the circumstances surrounding our last weasel (as we know whatever it was by). He was very young at the time, but still remembered the name of his farm cat that it had killed most quickly. I'd always thought it was finding a whole flock dead from 'em when I was little that caused me to pretty much despise 'em, but ... I don't remember the cat's name, but I still remember how much it hurt him to lose it in such a way.
I'll build/set traps for now, having had so few around here, but I'm gonna build new houses for my own flocks -- just to be sure.