During orthodontic treatment, the roots of the teeth might become shorter. It is not known exactly what causes root resorption but there have been suggestions that genetics may play a part. Dead teeth are also more prone to resorption.
Research has shown that tooth movement causes at least small changes in the shape and length of the roots in all orthodontic patients. In 98% however, these changes are undetectable with the naked eye.
At any rate, with the light forces used in orthodontics nowadays, the incidence of significant root resorption in hardly an issue.