Is it permissible and does it suffice to deduct the amount of zakat from the rent of a house leased to a poor family who cannot find their daily sustenance, by demanding from them the amount remaining after deducting the zakat?

Whoever's wealth has reached the nisab (minimum amount subject to zakat) and a hawl (full lunar year) has passed on it, must pay the zakat on his wealth to its rightful beneficiaries as mentioned in the Almighty's saying: "Indeed, [prescribed] charitable donations are only for the poor, the needy, those employed to collect [zakat], those whose hearts are to be reconciled, for freeing captives, for those in debt, for the cause of Allah, and for the stranded traveler – an obligation [imposed] by Allah. And Allah is All-Knowing, All-Wise." The obligation is to deliver the zakat funds to them directly or through an intermediary. It is not permissible to consider the forgiveness of a debt owed by a family as zakat, because it is not a real delivery of wealth.