Is it permissible to take charity money designated for public expenditure and deduct it from the debt of an insolvent person, and is it necessary to inform the debtor of this?

It is permissible to give Zakat and Sadaqah by proxy, but it is preferable for the owner of the wealth to distribute it himself. If you are appointed as an agent to pay Zakat or Sadaqah, you must pay it to those who are eligible, and it is not permissible for you to count it against debts owed to you by people, because Zakat is not valid unless it is transferred into the ownership of the poor person.

Furthermore, it is not permissible to waive a debt owed by an insolvent debtor with the intention of it being Zakat, for Zakat is a giving and a grant, not an absolution. The creditor should grant the insolvent debtor a moratorium until he can afford to repay. It is not permissible for the agent to take anything from the Zakat or to give it to the poor person on condition that the poor person returns it to him as a debt.