No food for the cat Until he/she finds the Rat and make it his/her meal.

Usually cats bring them to the door already dead, don't they? Seems your kitty needs a friend... new (additional) family cat in the future?

You might want to hurry and find it! My cat did the same exact thing, granted it was a mouse & not a rat, and the mouse lived inside for about a week. It used dryer lint to make a nest type thing in a cupcake pan. It was eating the dog & cat food. We would see things move in the corner of our eye and thought we were going crazy. It even made the cliche hole in the wall under the kitchen cabinets by somehow moving the wood slat over. After that week, we found it dead because our kitty killed it.

On one hand, a rat running loose in the house is unsanitary. On the other, your cat thinks you are ready to graduate from them bringing you pre-dead animals to eat, to them bringing you live ones to practice your killing on. Which means they are pleased with you!

Mine leaves rats for me in my bed. No just no.

standard cat behavior he brought home his food to play with it

Actually, when a cat brought a rat for you, it's a sign of them worshipping you. That's what they do with Pharaohs looooong time ago.