When domestic cats sleep in the “dead position” (i.e. they look as if they are dead) it’s because they feel sublimely secure in their home environment. They are belly-up and therefore vulnerable. I don’t think you’ll see this very often if ever in the wild. I’m referring to the wildcat ancestor of the domestic cat. If we want to understand domestic cat behaviour we always refer back to the wildcat within the domestic cat. It’s still there bubbling away waiting to come to the surface and show itself. Jackson Galaxy calls this the “raw cat”.
I think if your cat sleeps like this you should be pleased with yourself. I’ve seen cats do this in the middle of the kitchen floor. I’ve even seen a domestic cat do this in a public place, a restaurant. Particularly confident cats will do this more often whereas more timid cats will curl up on a cat condo or in a box in the dark somewhere.
When cats sleep in the classic curled up position, I believe that this is a throwback to the original tabby cat protecting themselves as they look like a snake. There are two points which support this (1) all domestic cats in the first approximate 3000 years of domestication were weakly marked mackerel/spotted tabby cats and (2) domestic cats are inherently aware of the dangers of the snake and have adopted some snake behaviours to protect themselves; such as hissing and curling up to give the impression that they are a snake to protect against predators who might harm them.
SOME MORE ON CATS SLEEPING: