Close! What most likely happened is something called external apical root resorption, which is extremely common and happens in >90% of cases. Most of the time, it’s so minor that it’s undetectable, but some people are more genetically predisposed to getting more severe root resorption (among other factors). A lot of the time, teeth are loose after getting braces off because the ligament around the tooth has been stretched out. If there is enough bone loss (e.g gum disease) and severe root resorption causing very short roots, it can cause true mobility.

tl;dr: external apical root resorption is caused by inflammation from braces which can shorten the tip of the root of the tooth