Is it permissible for the manager to sell my private property without my knowledge, given that he was aware of money that would be returned to him from other people, and that was in exchange for my taking a portion of the institution's money with the intention of returning it without his knowledge?

Possessing this money is invalid and constitutes consuming people's wealth by unlawful means. The money must be returned to its owners, for the Prophet, peace and blessings be upon him, said: "The hand is responsible for what it takes until it returns it." As for the institution's manager seizing your personal belongings, it is his duty to obtain his right through lawful means. If he is unable to do so, then he may take from your belongings an amount equivalent to his right.