I'd ask a vet and consider what you're feeding them. When I was a boy, we had some free-roaming cats that laired with us. We fed them, but they still went out hunting at night because that was their nature. They bought back dead rats for us and no doubt they sometimes ate bits of dead rat. Their breath was fine, didn't smell at all. Maybe your cat is ill or maybe your cat's diet disagrees with it. It's probably worth getting some expert advice about it.
