A tooth dies when its nerve and blood supply are cut off. When teeth are being moved with braces or aligners, some movements carry more risk to the tooth's vitality – for example, a tooth can die if it is rotated 180 degrees from its starting position. If movements like this are necessary, they must be carried out slowly and with light forces. Another way a tooth can die as a result of orthodontic movement is if the orthodontist applies very heavy forces. In principle this is not acceptable, and it is extremely unlikely.
This answer is for general information. Your own case needs an examination by an orthodontist.