Is it permissible for the zakat payer to disburse their zakat funds to settle the debt of their insolvent debtor?

It is not permissible to give zakat to your brother to repay a debt he owes you, because that would be a cancellation of the debt and an accounting of it as zakat, which protects your own money. However, it is permissible to give him zakat for him to repay debts he owes to others, or for him to use it for his other needs, if he is eligible to receive zakat.