All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Zakat is an act of worship like other acts of worship by which a Muslim gets closer to Allaah and it is one of the rights of Allaah so it is not permissible for a Muslim to pay the Zakat in a way to benefit from it himself and save his own money. Therefore, it is not permissible for you to pay the Zakat of your own money to someone who borrowed money from you so that he can repay you the debt from your own Zakat. However, if you pay the Zakat to him as a person who is eligible for Zakat and then he gives you some of that money as a payment on his debt to you without a mutual agreement between yourselves, or cheating in order to get back the debts, then it is permissible as Ibn Qudaamah stated in Al-Mughni reporting from Imaam Ahmad. It is also not permissible for you to drop the debts of anyone in return of the Zakat money as in such a way you are the one who benefits from the transaction and the Islamic jurists have stated that it is not permissible to drop the debts from the debtor and consider that as Zakat.
Allaah knows best.