That's interesting. I've experienced something similar to this when falling asleep with audio playing. I'll continue to hear the audio while I'm dreaming and a visual representation of what I am listening to will arise in the dream state.
It's subtly different then what you're describing, in that the visual aspects of the dream aren't a continuation of the film, but usually an imaginal representation of what I'm listening to. If it's music, I might find myself at a concert or watching a music video in the dream. If it's an interview, my dream might manifest as a conversation. When this happens with an audiobook, the dream will often be a visual representation of the story to accompany the reading.
I can't recall this ever happening with films in the way that you describe, but I don't often fall asleep while watching video. I might try to force myself to fall asleep while watching something and see if I can experience this.