Are the extra funds that the company mistakenly deposited into my relative's account, and which he spent in their entirety, permissible for him, knowing that the company is recovering them from him through monthly deductions from his salary?

It is not permissible to use the surplus money in the salary before knowing its source. Whoever finds surplus money in their account without a rightful claim must repent to Allah and return it immediately, or by installments if the company agrees and they are unable to return it in a single payment. They are not allowed to procrastinate, for the Prophet, peace and blessings be upon him, said: "Procrastination of a rich person is an injustice," and "The procrastination of one who can pay makes his honor and punishment permissible."