1. Loose Bracket- The bracket comes loose from the tooth (very common). It usually stays attached to the wire but tends to roll around or move some. This is usually not an emergency. The bracket (or a new one) can be re-bonded at the next orthodontic appointment (hint--let the office know ahead of time).
2. Wire poking - Sometimes the wire slides around to one side and can cause discomfort in the back part of the mouth and cheek. This seems to occur in the earlier stages of treatment when the teeth are beginning to move and the wire straightens out. However, it can happen anytime. Usually the wire is clipped off or the wire slid back around into place with a simple adjustment.
3. Appliance Loose/Off- Sometimes an orthodontic band, space maintainer, expander, or other dental appliance may come loose from the tooth. If only one part or side is loose, it often just moves up and down, but can be re-cemented. Sometimes the appliance is damaged and needs repair or replacement.
4. Band Broken or Appliance Damaged- Orthodontic ligatures, bands or other attachments can become damaged and create an ulcer on the soft tissues of the cheek, lips or tongue.
5. Traumatic Injury- If the lips are traumatized into orthodontic hardware, they can become "stuck" in the braces. A gentile tug can free the lip. Otherwise, the dentist can free the tissue. Braces can actually protect the teeth in cases of major trauma, preventing teeth from being knocked out or more severely displaced.
Of course, in all cases I recommend contacting your Pediatric Dentist or Orthodontist.