Root shortening refers to resorption of the tip of the root inside the bone, which can only be seen on an X-ray. There are normal limits within which this kind of shortening affects individual teeth in the mouth – around 1 mm does not affect the health of the teeth. Root shortening occurs in some people who have thin tooth roots and are predisposed to it, and also with certain movements, such as intrusion of the front teeth (moving upper teeth upwards or lower teeth downwards, towards the gum); when excessive forces are applied to the teeth; when elastics and archwires are changed too often (more often than once a month); and in dead (root-filled) teeth, which are additionally predisposed to this process. Within the limits of normal shortening, there will be no harmful consequences for the teeth.
This answer is for general information. Your own case needs an examination by an orthodontist.