Is it permissible to waive the rent owed by an insolvent tenant and count it as Zakat, and is it obligatory to inform him of that?

A condition for paying Zakat (definition) is that the poor person takes ownership of it. Therefore, it is not permissible for Zakat to be a debt annulment for what is owed by the poor person. This is the view of the majority of jurists, because Zakat is a liability (in one's trust) and is not discharged except by its physical handover, and because Zakat is Allah's right, so it is not permissible for a person to use it for their own benefit. However, if the poor person is given Zakat and uses it to pay rent or a debt without any prior condition or trickery, then there is no harm in that.