Is it permissible to take an unknown surplus amount and spend it, then return it from the employee's private funds when its owner appears?

You are entrusted with the money under your control, and it is not permissible for you to dispose of it except as you have been instructed, in your capacity as agents for the bank. Any increase whose cause you do not know must be added to the money until its owner or cause becomes apparent, or until you inform the responsible party. It is not permissible for you to take any of it without their permission. Whoever takes anything from it will be held accountable for it and will bear the sin of betrayal.

If the increase results from an error by customers or a lack of proper exchange, the money remains the property of its owners. If its owner is not known, it takes the ruling of found property (luqatah). If the bank holds you liable for a deficit without any negligence on your part, then it is permissible for you to take from the existing surplus an amount equivalent to this deficit. This is known as the issue of al-Zafar.