Many people don't close the interior doors when they go to sleep. They find it more pleasant when the doors are open, or it is for a practical reason:with the doors open you can hear the children better. Still, it's better to close the doors.
If a fire breaks out, you increase your chance of survival if the doors are closed. With open doors you hardly have any chance of survival after 3.5 minutes. With closed doors, that can even be ten minutes. It is also important that you place smoke detectors in your home.