Is it permissible to wear trousers without a belt, letting them sag? Thank you.

The main consideration regarding wearing trousers is whether they adequately cover the 'awrah (private parts). If they lead to the exposure of the 'awrah, then wearing them is forbidden; otherwise, it is not. Furthermore, one must consider avoiding imitation of disbelievers and transgressors in the manner of dress, based on the general statement of the Prophet, peace and blessings be upon him: "Whoever imitates a people is one of them."