So, when I put my hand on her neck gently, as she's just borderline sleeping, she'll start making 'heavy breathing' noises and gently fall asleep. Kind of like a cat purring. My wife calls it the "hand of dad" effect -- and it's really sweet -- she's done that since she was tiny pup; but I haven't seen any mention of dogs 'purring' -- she's clearly super relaxed and it's clearly a happy noise, but I never heard of it!
Gratuitous pic of the victim: