Cats are very shy animals and will not just lie down next to strangers or unfamiliar people. If a cat sleeps next to you, it must trust you very much and feel safe around you, knowing that you are not Will hurt it. The different sleeping positions of cats next to people can show the different needs of cats for you: cats sleep near their heads to become familiar with your scent; sleeping with you in their arms shows that cats regard you as a relative.