The answer is: No—neither for an obligatory fast nor a voluntary one. Even if a person is incapable of fasting and owes an expiation for a broken oath, or the compensatory fast for harm—fasting three days—such as an elderly man who has children and says to them, “Fast three days on my behalf,” this does not suffice for him. That is because this has not been reported from the Prophet, peace and blessings be upon him. When it has not been reported, then—as we have said—the basic principle regarding acts of worship is that appointing another to perform them is not permissible, because it defeats the purpose of worshipping Allah. Therefore, if an incapable person appoints someone to fast on his behalf, it does not suffice if his incapacity is not expected to end. But if he appoints someone to feed people on his behalf, this suffices, because feeding is analogous to zakah.
If he dies, should the fast be made up on his behalf or not? As for a voluntary fast, it is not made up on his behalf, because this has not been reported. Since it has not been reported, the basic principle is that it is not to be made up. Thus, if a person customarily fasted the three white days but did not fast them, then died before the month was complete, no one should fast them on his behalf.
If it was obligatory, some scholars held that it should not be fasted on his behalf, because if he dies without having fasted, he is like an elderly person or one suffering from an illness from which recovery is not expected. One needy person should therefore be fed from his estate for each day, and no fasting should be done on his behalf.
Other scholars held that obligatory fasting should be performed on his behalf, whether it was obligatory by the original prescription of the Sacred Law, such as Ramadan, compensatory fasting, and expiation; or obligatory due to a vow. They cited the Prophet’s statement in the hadith of Aishah, may Allah be pleased with her, recorded by al-Bukhari and Muslim: “Whoever dies owing fasting, his guardian should fast on his behalf.” (1) His words, “owing fasting,” include both an obligation established by the Sacred Law itself and an obligation arising from a vow; thus, the wording is general.