In Islam, a missing person cannot be considered dead unless a court decrees so. In this case, the property left by that person can be distributed among the heirs according to the Islamic law of inheritance.
Responding to the question, Dr. Monzer Kahf, a prominent economist and counselor, states the following: Whenever we cannot determine the times of death of people who inherit from each other, we assume that they die at the same time. This means that persons who lived in one city or the same distance from the disaster are assumed to have died at the same time; the estate of each one of them is distributed to his or her surviving heirs on the assumption that the other did not exist at the time of death of the person whose estate has been distributed.
Moreover, the eminent Egyptian scholar and renowned da`iyah Sheikh `Abdel Khaliq Hasan Ash-Shareef, adds: The local court has to issue a decree indicating that such-and-such person has died after exerting all possible efforts to find him or her. If there is no way out and the court has issued its decree, then there is nothing wrong in distributing the remaining property, giving each heir his or her due share. In case the dead person was a married man, it is permissible for his widow to remarry after the final decree of the court is issued.