The bond between a bracket and tooth enamel is the strongest; next comes the bond between a bracket and a light-cured composite filling. The bond between a filling and the tooth is stronger than the bond between the bracket and the filling, so a bracket cannot pull a filling off while it is moving the tooth. If this happens, it simply means the filling hadn't held well to the tooth and needs to be redone.
This answer is for general information. Your own case needs an examination by an orthodontist.