They would have a basic history of remembrance. Just like how RPs start out, your character is usually a semi foggy slate. It's not 100% blank, you have an idea of where that character wants to go and thus made a few lines for their past to go off of. 

I was trying to have that be open to you guys as too how much your character would remember and see if it can reflect on their current situation. Would it be a assassin who is confused and wondering why he is no longer in his slum city apartment? Or would it be a student who has knowledge of subjects but no idea where they got said knowledge?
Or even, as you said. Would it be like Kingdom hearts and be a lifeless doll like Roxas was and needs to wake up bit by bit? So long as they are not given a keen advantage, like seeing the creator's next move, than the choice is up to you. 

And I'm just glad we're fixing things up and stepping in on the same RP.