I'm not sure exactly what you are trying to say...A well fed cat won't be bothered with hunting and the it's only little scurrying or flapping prey animals that produce the hunting reaction from domesticated cats. I've raised many chicken and quail chicks inside and our cats never worry them in the least, yet we've had a few mice come inside and they have been hunted down and caught by our two cats. And I would never have the cats in the same room when we let our finches and parakeets out for some exercise because their small size and furious flapping
My friends well fed cat hunts and brings him small birds and rodents all the time. Cat has access to feed 24/7. I saw a documentary where they strapped cams on cats to see their daily lives. And I don't remember the exact numbers, but... a percentage of cats still hunt, just for fun.
One night I saw two cats messing with a mouse/rat (I couldn't tell) but they just kept slapping it around and basically torturing it. Can't say those were well fed or not... but they were in no hurry to eat it.