When I had my great danes, I loved them, but I must have a real cold spot in my heart because I occasionally thought that if it came down to it, I had a lot of meat walking around in my yard. I honestly think it would be kinder if we did give them a merciful end rather than turning them out on their own if they don't have an instinct to hunt. Most dogs that go wild will form a pack and that can be very dangerous to humans in a very hungry world.
As for cats... I, too, have allergies, which is why I have a rex cat. They are the "poodle" of cats with hair rather than fur. She looks like the bald cat from The Book of Eli with short hair that's been stuck in a crimping iron (that movie cat was actually a Sphynx - a registerable breed of cat). I wouldn't go so far as to extract cat oil from her as Eli did, but I would quickly put her out of our misery. I barely tolerate her now, not because of her hair but because of her attitude. She's only 4 pounds and not in the best of health anyway so I'd just bury her, not eat her.
Does anyone remember the dog food recalls some 6-7 years ago when pets were dying all over from tainted pet food? I lost 3 to that and began an intensive research of animal nutrition. The diet that made the most sense to me was actually called B.A.R.F. - Biologically Appropriate Raw Food. In the wild, if a dog kills and eats a rabbit, it will get at least 60% meat and bone and the other 40% consists of everything from heart, liver, kidneys, vegetation, grain, possibly fruit and herbs from the stomach. I put my dogs on that diet for as long as I could afford it. Every day, they had chicken (meat, bones, heart, gizzard, etc.), spinach, apple, eggs, yogurt, brown rice, garlic and I can't remember what else I put in it without consulting the book.) Within 2 weeks of starting that diet, I saw improved everything from coat texture and brightness of the eyes to their ability to focus in training and their energy was more positive and contained. If I'd had a livestock farm at the time, it probably would have been much less expensive. And that's my point: if you have livestock and a garden, your dog will get all the nutrition it needs without commercial dog food (cats, too). If you don't have a farm, are you prepared to hunt specifically to feed your dog? Or, are you willing to teach your dog to hunt for itself? Big dogs can help bring down game that will feed both you and them.
Since the advent of commercial dog food in the late 20's early 30's, the lifespan of all dogs has shortened. Prior to then, the average lifespan of a dog was 17-25 years. Much of the crap they put in dog food they aren't even able to digest, specifically corn (and GMO corn, I believe, is a primary cause of cancer in pets as well as humans). There was even a point where they were including as ingredients the euthanized bodies of animals from dog pounds and simply calling it "meat." Table scraps are far healthier for your dog than any dry food you can buy.
One more myth down the drain - raw chicken bones are very good for your dog. From the time of the recalls to when I recently gave away my last dane, every one of my dogs had 2 raw chicken leg quarters every day as the most important part of their diet. Any type of bone cooked can splinter and damage your dog internally, but raw bones are very easily digested by a dog's rapid, acidic digestive system.
Keep in mind that if your dog is going to eat a raw diet, it needs 8% of it's body weight daily to maintain health and energy.