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.
Zakat (Almsgiving) is paid only to eight types of people who are identified in the Quran, as Allah Says (what means): {Zakah expenditures are only for the poor and for the needy and for those employed to collect [zakah] and for bringing hearts together [for Islam] and for freeing captives [or slaves] and for those in debt and for the cause of Allah and for the [stranded] traveler - an obligation [imposed] by Allah. And Allah is Knowing and Wise.} [Quran 9:60
Thus, if the people afflicted in those disasters were Muslims who were characterized by these characteristics or some of them, then they are eligible for Zakat because they are among its legitimate recipients. This is what is most likely to be the case with regard to those Muslims who are affected by earthquakes or other disasters, that they become poor without shelter, food or clothing, and there is no doubt about the permissibility of paying Zakat to these people. On the other hand, if someone of them did not become poor in those disasters and remained rich with his money, with which he could afford to spend on housing, food and clothing, then Zakat would not be paid to him as being poor.
Allah knows best.