Is it permissible for a private institution to agree with workers to employ them for 200 dinars per month, while requiring them to collect 250 dinars from the bank designated for the unemployed, and then pay the institution 50 dinars, under the pretext that the difference is used for the public good?

If the private institution is an agent of the governmental institution, then it is not permissible for it to pay 200 riyals to the workers while the principal requested 250 riyals, because that is considered taking people's money without their consent. However, if the private institution is an employee (hired by) the governmental institution, then it may agree with the workers on whatever wage it wishes, and the governmental institution does not have the right to restrict it to a specific wage, unless this restriction is from the state for a valid, legitimate interest.