What is the ruling on a woman continuing to work in an institution that prohibits the hijab in order to pay off a debt she owes, knowing that her husband cannot cover the debt installments?

It is legally forbidden for a woman to expose her 'awrah (intimate parts) to non-mahram men. A woman is not permitted to engage in work that prevents her from covering her 'awawrah from non-mahram men. Whoever gives up something for the sake of Allah, Allah will compensate them with something better. A woman must adhere to the hijab and stay away from forbidden things. If she is dismissed from her job because of her hijab, then she should look for a lawful job that does not entail falling into the forbidden. If she is compelled to work in a job that requires exposing her 'awrah due to debt and cannot find any other work, and fears harm due to non-payment, then this work is permissible for her out of necessity, which is estimated according to its extent. She must continue searching for an alternative.