Is it obligatory to report a deficit that occurred inadvertently in the sale of books at a library, knowing that reporting it to the supervisor, who is known for injustice, will lead to a salary deduction, and am I responsible for this deficit?

If you did not exceed your bounds nor fall short in your work, then you are not accountable for the resulting deficiency, and you are not obligated to inform the bookstore owner. This is because you are a specific employee (ajir khass), and a specific employee is considered trustworthy and is not liable for loss unless there is transgression or negligence, according to the majority of scholars.