LPT: If it's asleep, rub the appendage. Anecdotally it seems to work for me. Like for example, if its my arm, I just take my other arm and rub up and down the length of it as if to stimulate circulation.

When something goes to sleep, I have heard that it's not a blood thing, but a nerve thing. My pet theory therefore, is that while you probably are stimulating some blood flow to some capillaries that were squeeze shut with pressure, it's moreso works because you're stimulating nerves or some bullshit. Also doesn't hurt that just massaging a limp appendage is a little more calming than panicking.