Praise be to Allah.
If someone goes missing or disappears completely, and no news is known about him, and it is not known whether he is alive or dead, if it appears from the way in which he disappeared that he must have died, then the majority of the scholars are of the view that his family must wait for four years from the time of his disappearance, after which the judge may rule that he is to be presumed dead. In that case, his wealth may be divided and his wife should observe ‘iddah.
Abu Haneefah and ash-Shaafa‘i, in his later view, were of the opinion that he cannot be presumed dead unless there comes news of his death, or he reaches an age where he could not still be alive.
See: al-Mughni (8/131) and al-Mawsoo‘ah al-Fiqhiyyah (29/333).
The majority of scholars quote as evidence the report from ‘Umar ibn al-Khattaab (may Allah be pleased with him), which says that in the case of one who went missing, he ruled that his wife should wait for four years, then her husband’s next-of-kin should issue a divorce (talaaq) to her, whereupon she should observe ‘iddah for four months and ten days, after which she would be free to remarry. Narrated by al-Bayhaqi (7/445); its isnad was classed as saheeh by al-Albaani in Irwa’ al-Ghaleel (6/151).
Imam Ahmad (may Allah have mercy on him) said: Whoever decides not to follow this view, what view can he accept when this is the view of ‘Umar, ‘Uthmaan, ‘Ali, Ibn ‘Abbaas and Ibn az-Zubayr?! Ahmad said: These are five of the companions of the Prophet (blessings and peace of Allah be upon him)." (Al-Mughni 8/131).
The scholars listed some of the ways in which a person may disappear, after which it may be assumed that he has died:
If someone went missing from among his family, by night or by day, or he goes out to pray and does not return, or he goes to a nearby place to relieve himself and intends to come back, then no news is heard of him, or if he goes missing on the battlefield, or if a boat sinks and some of his fellow passengers died, or he goes missing in a wilderness, such as the desert of the Hijaz, and the like." (Al-Mughni).
A judge referred to Shaykh Muhammad ibn Ibraaheem regarding the case of a man who went missing during the night of coming down from ‘Arafah at the time of Hajj, and he had a wife and an estate. Is he more likely to be dead or alive?
He replied: Please note that the way in which he disappeared suggests that he is most likely to have died, because the one who disappears on such a night is vulnerable to the dangers of stampedes, collisions and sickness as a result of sunstroke and the like, which are regarded as reasons for what we have mentioned, that his disappearance most likely means that he has died." (Fataawa Ibn Ibraaheem 9/264).
Regarding the question about offering the funeral prayer for the two missing men, the funeral prayer may be offered for them in absentia, because it is most likely that one who has gone missing for such a long time has been killed or has died, especially since there is news that your brother has been killed, as mentioned in the question. If it so happens that in fact he did not die and was not killed, then the matter of offering the funeral prayer in absentia is not a serious matter, and it does not result in anyone missing out on his rights or any transgression of the limits set by Allah. Shar‘i rulings may be based on what is most likely to be the case, and the purpose of the funeral prayer is to offer supplication for the deceased and seek forgiveness for him.
There are other rulings which result from the assumption that a person has died, such as the division of his estate, and it becoming permissible for his wife to remarry after completing the ‘iddah that required following the death of the husband, and so on. With regard to these rulings, it is essential to have a verdict from the judge that the man is to be presumed dead, so that though will be no confusion or transgression of people’s rights.
Shaykh Ibn ‘Uthaymeen said, regarding the case of one who has gone missing:
It is essential to get a verdict from the judge, lest people end up in a chaotic situation. That is because if we say that any woman whose husband goes missing may wait for a period of time after which she thinks it most likely that he has died, after which she may remarry, that would lead to chaos … It is essential to refer to the judge, and he is the one who should take care of this matter. This is a must." (Ash-Sharh al-Mumti‘ 13/374).
For more information, please see the answer to question no. 2313 .
And Allah knows best.