Rendering processes are used to produce raw sources of fat and protein in pet food; you can tell if your food has it by the word meal or by-product on the ingredient label. Just about every cat food has fish meal, chicken meal, poultry by-products, or something to that effect. "Fish meal" does not mean "contains only fish," it means "contains mostly fish." Rendering is highly unregulated, and due to labor costs, much plastic and styrofoam enters the process as expired/rotten meat packages from supermarkets are tossed in, still wrapped in the package.
Euthanised pets are far more commonly used than you would think, it is not an exaggeration to say that your cat and dog food contains actual cat and dog. They come in green plastic bags which are not removed. They are generally loaded with barbiturates used in the euthanasia process, and no, the drugs are not destroyed by heat. Cows are rendered; they often have plastic insecticidal patches that are not removed either. Metal ID tags enter the process as well.
Rendering plants are most likely the largest source of contamination and infection that helps spread normally rare diseases like spongiform encephalopathy -- mad cow / mad deer / mad sheep / Creutzfeld-Jakob Disease. In fact, it is nearly impossible to be infected with prions without eating other animals, and it is suspected that brain matter must contaminate the meat, as is the case when entire animal carcasses are tossed in. Much of the rendered meal also goes into food fed to otherwise herbivorous animals like cows. And even zoo animals are used -- you can count on the occasional giraffe and elephant products in your cat/dog food, and the meat you eat (unless it's organic / free range) was probably nourished on cows fed with animal by-products and chicken feces.
England recognized rendering processes as the sole cause of escalated cases of "Creutzfeld-Jakob disease", "mad human disease" and has ordered that cows no longer be fed meat by-products. Cases are still popping up throughout Europe, and many Americans have fallen victim as well. At least two people have died of spongiform encephalopathy after eating venison, but no proven link has been found since they ate other meat regularly as well.