The one Lego Advent calendar I bought didn't have little boxes. Each day's model was in a plastic bag, with a picture of the assembled model on the front. There were no instructions for the daily model, but there were instructions for how to combine four or six models together into a different model. I don't remember how the cardboard box was set up... there must have been little doors to open, with the bags inside the doors? I cut the bags open carefully and we still have them, and all the Legos, though most of the Legos have been mixed into the general pool.
This was years ago, though, so the calendars may be different now.
Even though my kids are teens, I am tempted to buy the new Playmobil calendar... or maybe one of the Lego calendars. :)