Securing the coop the BEST YOU CAN is the best choice. A baby monitor may help,,,,,, but I think that when you hear the distress,,,,, it may be already too late,,, or a false alarm also.
The way you describe the chicken,,, it may have been the work of a opossum.??? A small to medium one possibly.

Cats can be predators of chickens, but not very often. I know there will be a swarm of different opinions flowing from many different peeps out there.
I have a Number of feral cats on my grounds,,,, and none of them bother my chickens. They did show much interest in baby chicks BTW, and also My Pigeons. They left my small banties alone for some reason even they were smaller than my pigeons. Serama Chicken in my avatar.
WISHING YOU BEST,,,,,,,,,,,,,,,,,,,,,,,,,,,