It depends on the cat. I used to work with rats in research labs so I know their abilities and size well. They are unusually smart small animals and pretty good fighters but tales of huge rats are exaggerated. No domestic rat approaches the size of anything but a kitten a few months old. If you think you have a place where rats get big and mean enough to defeat a cat, my daughter has a cat that would politely disagree with you (probably just before slashing your your throat from behind).
Her cat is as sweet as can be to people but he lives to hunt and kill. His record is five full grown squirrels in an afternoon but he also like to mix it up with chipmunks, rabbits, rats, mice, and he even stalks wild turkeys that come into the yard but that always ends in a standoff. He is the best hunting cat I have ever seen however. Not all cats like to fight much and a few rats do so you could see a small cat get get defeated by a really aggressive rat if the circumstances were right but I wouldn’t count on it.
If you want to take the rat idea to the extreme, nutria are rodents that live in the swamps of states like Louisiana and can kill a dog much larger than themselves. I was with a man that had his Golden Retriever attacked by one on a duck hunt once. The dog survived the immediate attack although it was a brutal mess of internal injuries but died of complications at the vet a few weeks later.