All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
In principle, a Waqf (Religious endowment) must remain sustainable and uninterrupted because it is limiting the benefit of an endowed property to eligible beneficiaries, and not to the donor. Dedicating the benefit of the Waqf in the cause of Allah is a charity that brings the donor closer to Allah. Thus, if the Waqf revenues were limited to the children of the donor, and the first generation/layer of them has become extinct and the donor haven`t stated that the revenues are to be passed to the following generation, then, in this case, it must be passed to that generation. However, this means including maternal and paternal relatives as well as the Asabat and others. Yet, they are distinguished in accordance with the degree of kinship and not inheritance. Therefore, preference is given to the daughter`s son over paternal uncle`s son because the daughter is closer than the paternal uncle in the degree of kinship. Moreover, the poor relatives are also eligible beneficiaries of Waqf revenues.
Al-Shribini (May Allah have mercy on him) said: "If the donor said that the Waqf revenues are to be given to his children and they became extinct, then, according to the reliable opinion, the Waqf, in principle, must remain sustainable and uninterrupted…. After that, the revenues are given to the relatives of the donor because charity given to relatives is amongst the best deeds that bring a Muslim closer to His Lord. Allah`s Messenger said: "Giving charity to a poor person is charity, and (giving) to a relative is two things, charity and upholding the ties of kinship."" {Moghni Al-Mohtaj, Vol.3:P.536}.
In conclusion, the revenues of the Waqf must be divided amongst the donor`s poor maternal and paternal relatives, be they children of females or males of equal degree of kinship. However, preference is given to a close relative over a distant one, even if the latter is an Asabah. For example, a daughter`s son has preference over a maternal uncle`s son. And Allah the Almighty knows best.
[1] Asabat are the sons; then their sons; then the father; then the grandfather; the then father's sons i.e. brothers; then the grandfather's sons i.e. paternal uncles; then the sons of the grandfather's father.