All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
A person who guarantees a debt for a creditor must pay the debt if the debtor is unable or fails to pay it. The creditor has the right to demand payment from either the debtor or the guarantor, whichever they choose. It is stated in the [Hashiyat Al-Bajuri, Vol.2/P.726], a book from the Shafi'i school of thought: "The creditor has the right to demand the debtor or the guarantor, whichever they choose, for the full amount of the debt."
Actually, Allah has mentioned in the Glorious Quran the eight categories eligible to receive Zakat. He, Allah The Almighty Says (What means): "Alms are for the poor and the needy, and those employed to administer the (funds); for those whose hearts have been (recently) reconciled (to Truth); for those in bondage and in debt; in the cause of God; and for the wayfarer: (thus is it) ordained by God, and God is full of knowledge and wisdom.." [At-Tawbah, 60]. Zakat must fulfill certain conditions to be valid, including transferring the ownership of the Zakat to the deserving recipients, which is inferred from the particle "lil/for" in the above verse. Another condition is the intention (Niamh) at the time of giving the Zakat. Imam Nawawi, may Allah have mercy on him, said: "Intention is necessary. One intends 'This is the obligatory Zakat on my wealth' or 'This is the voluntary charity from my wealth,' and the like." [Minhajj At-Talibin, Vol.2/P. 72].
One of the conditions for Zakat to be valid is that it should not be given to oneself, as giving Zakat to oneself is not considered a valid disbursement or ownership. This is because one can`t be a giver of Zakat and a recipient of it at the same time. In addition, Zakat shouldn`t be given to those whom the giver is obliged to provide for (dependents), even if they are poor or needy. Imam Ash-Shirbini, may Allah have mercy on him, mentioned in his explanation of those who are not eligible recipients of Zakat: "The fourth category is someone whose expenses are covered by the Zakat payer due to marriage or an extension of that relationship (Such as being a son or daughter). The Zakat payer isn`t allowed to give them Zakat even if they are poor or needy because they are self-sufficient by his providing for them. However, he is allowed to give them Zakat from the share allocated for the remaining categories if they fit into that category" [Al-Iqna' Fi Sharh Alfiyyat Abi Shuja', Vol. 1/P. 232]. In fact, giving Zakat to settle a debt that one is legally responsible for paying is similar to giving it to oneself, therefore, it is not permissible.
Therefore, it is not permissible to consider what the guarantor has paid due to the guarantee as part of Zakat, as it violates the condition of intention at the time of disbursement and the condition of ownership. However, there is no sin on the guarantor to pay from their Zakat for the guaranteed person as a debtor or as a poor or needy person. Also, the guaranteed person, after acquiring the Zakat, can settle their debt from it if they choose to do so. And Allah The Almighty Knows Best.