If husband can not pay mahr during the life of wife, does he need to pay the mahr even after her death? What is the rule for that?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

This deferred dowry is a debt which the husband is obliged to pay, and he is not exempted from this obligation due to her death. It is among the inheritance of the deceased woman.

Abu Hurayrah narrated that the Prophet said: "Whoever leaves any wealth, it is for his heirs." [Al-Bukhari and Muslim]

Whenever the husband becomes solvent, he must pay it to her heirs so that it can be divided between them according to the Sharee’ah.

Allah knows best.