Is it permissible to take money designated for housing from the government and not use it for that purpose?

The reference for housing allowance issues is the system of the granting entity. If the student is absolutely entitled to the housing allowance, regardless of their need or its cost, then there is no harm in benefiting from it for purposes other than housing rent. However, if they are entitled to it on the condition of need and its expenditure therein, then it is not permissible to spend it on anything other than housing rent.