I don't know if this happens to other writers.
Not always, but often enough that I can say it happens, I have a dream with a letterbox edge along the bottom--as if for subtitles. Across this black edge a hand writes what's happening in the dream. Stage directions, description, lines of dialogue. It's not like a play. It's prose.
Sometimes the hand scratches out words and the scene has to start over again. A character gets axed or dialogue rewritten. The hand doesn't write quickly, but at an unhurried, flowing pace. Action happens at an ordinary pace too. The hand can keep up because it doesn't record everything, only what it decides is pertinent. Somehow--in dream reality--it all works out.
I don't think I'm the person writing the dream. I feel more like the person responsible for getting it down. When I have a dream like this, I wake feeling tired. You bet.
Since I write first draft longhand, I'm not surprised by the pen. However, I'm left-handed, and the dreams are always written with the right hand and in a script that is not mine. I can't get a good look at the hand because it's always moving, writing. Don't know if it's mine.