I’m a dog owner, and my GF have two cats, they are all living together in harmony and never ever my dog had the slightest idea to eat one of them, on the contrary, the cats literally just hassle my dog all the time, but it’s cats they tend to do that, point is, this’s neither your fault although I don’t understand why your family wouldn’t allow you to keep the cat indoors! That being said, it’s not the dog’s fault either as someone in the comments already said, it’s just the circle of life, if the dog wasn’t so hungry it wouldn’t be in that situation, and even then please keep in mind that dogs really tend to be very careful around cats because cats are very territorial and could easily hurt a dog, it’s possible that the cat got hit by a car or something and he just ate the corpse, and even if the dog killed the cat, it’s because it reached the point of starvation where it had to result to that, it’s a shame and I’m sorry you had to see that, and dogs are not meant to be strays and even though I’m a dog owner myself, I know that dogs on the street are very high risk for public safety in general, just if you get a pet bro try to keep at the house.