What is the ruling on giving goods that are not rightfully his to a supervisor who requests them to work with, knowing that he will obstruct the work of the institution if they are not given to him?

As long as the supervisor is not entitled to take goods, it is not permissible to give him anything from them, as this involves betrayal of trust and unlawful consumption of property. If this leads to obstructing work and harming the institution, then the matter should be escalated to the officials.