The rubber band that stretches around your bracket is known as the "bracket ligature band." It has an important purpose. The band holds the wire to the bracket, creating the pressure that moves your teeth. In some cases, a type of twisted wire will be used, but rubber ligatures are the most common.
If the ligature does come off, you can try to replace it with a pair of sterile tweezers. You can sterilize metal tweezers by boiling them or soaking them in rubbing alcohol. A wire ligature can be removed with the sterile tweezers.
If you have a wire ligature that is sticking out and poking your lip, you can use either a cotton swab or a pencil eraser to try to bend it back into place.
We'll need to check a loose or lost ligature, so if this happens, please give us a call so you can be seen. Once one ligature is lost, it's likely that you may lose others. Without the ligatures in place, your braces won't do their job properly. We will likely need to replace any lost ligatures, and you may need an adjustment as well to make sure that your treatment stays on track.