Curled Up: Felines who curl up in a tight ball with their tail wrapped around their bodies are doing what comes natural to them. Cats in the wild will sleep this way as it offers protection and conserves body heat. It is one of the most popular sleeping positions for domestic cats, especially for cautious or nervous felines.
Contortionist: Felines that look like a twisted pretzel when they sleep are very comfortable in their surroundings, even if they don’t look like it. There is no real reason as to why cats will sleep in what appears to be uncomfortable positions, unless they are truly comfortable with their heads hanging off the edge of the chair. These weird cats love attention and maybe that is why they choose this position.
Belly Up: Cats who choose to sleep on their backs with their bellies up are confident and feel secure in their environment. The vulnerable position exposes the feline’s vital organs and is harder to jump up from, so cats who sleep this way have complete trust in their owners. Friendly indoor cats are often seen napping this way. It is almost as if they are begging for a belly rub.
Burrower: How many times have you found your cat napping under a blanket, behind a pillow, or inside a box? Cats love comfort and being warm and this position provides both. While any cat can burrow from time to time, if your cat always naps under something they may be chilly or seeking security. Shy cats will often find a good hiding spot to nap and prefer to be left alone.
Jesus: Hey, Dad? God: Yes, Son? Jesus: Western civilization followed me home. Can I keep it? God: Certainly not! And put it down this minute--you don't know where it's been! Tom Robbins in Another Roadside Attraction
do not give that belly rub unless it is your cat and you know for a fact your cat wants and/or is expecting a belly rub. Waking up a cat that way, unexpectedly, can result in activating all four sets of claws, because that is a defensive reaction. I had a cat that passed away earlier this year, I still miss her terribly, who slept like a dead cat, all over the place, on her back, legs splayed; first time I rubbed that belly she sank teeth and claws into my hand. After that, she expected that belly rub, and I wish I could still give her one.
America is not a country, it's just a business. (Brad Pitt, Killing Them Softly)
Everything I post is just my opinion, and, honestly, I would love to be wrong.