Yes. Ours do that.

Cindy just recovered from a DVT. When she was first diagnosed with the clot they sent her home and she was to be fast in bed. Lamoni (our giant boy cat) was always on the bed with her.

"He is our angel." I think that cats know way more than we generally give them credt for. Anytime that there is a tense scence on TV and we get excited he comes to our feet and wants to be petted at the food bowl. He does this to distract us because was are always calmer when we are petting him.