When I'm in that state, I don't remember old dreams, I create new ones that blend in with what's happening around me. Like I see that I'm talking to a frog, but the frog is saying everything on the TV that's still playing.
I get that too right before I fall asleep! At least when I'm sleeping in public. My brain distorts and abstracts what's going on around me into a weird half dream. Then I fall asleep.
I don't get to read much anymore, but I used to be reading books at basically all times. Many times I've fallen asleep, book in hand, and continued reading a book that - it would turn out - had nothing to do with the book I was holding.
Sometimes, I wouldn't even have to turn the pages. Instead, I would just continue reading the other side of the page in front of me.
On occasion the story was much more interesting than the one the book actually presented.