We're closer to zombies being real than you may think, all it would take is for a carnivorous or omnivorous animal to have both rabies and a prion disease at the same time. Both can easily be transmitted by saliva and biting, and prion disease eats away at the brain, meaning the "zombies" wouldn't eat your nervous system, but the disease would, slowly and painfully. Not so fun fact that's also extremely worrying if you think about it