Is it permissible to fast extra days beyond what is prescribed by religion to make up for missed fasts for a deceased person with whom I have no kinship?

In the Sahihayn, the Prophet, peace and blessings be upon him, said: "Whoever dies and owes fasts, his guardian should fast on his behalf." This is evidence for the permissibility of fasting on behalf of the deceased if they owed fasts, whether due to a vow or an obligatory duty by the original divine law. If the deceased was unable to make up the fasts, then no one should fast or feed on their behalf. However, if they were able to make up the fasts, then it is recommended for their guardian to fast on their behalf.

Scholars have differed on whether it is permissible for someone other than the guardian to fast on behalf of the deceased. Al-Bukhari leaned towards its permissibility, and the preferred view is based on the Prophet's, peace and blessings be upon him, comparison of fasting to a debt. A debt can be repaid by anyone. The guardian was mentioned because they are usually the ones to do it, and because the preponderant view is the permissibility of donating the reward of physical acts of worship to the deceased.

Al-Hafiz mentioned in Al-Fath the difference among those who permit it regarding the meaning of "guardian." The apparent understanding from Al-Bukhari's action is that fasting is not exclusive to the guardian. So, if a deceased person asked a stranger to fast on their behalf, it would be sufficient, or if a stranger independently undertook it, it would be valid. What Al-Hafiz favored is the Prophet's, peace and blessings be upon him, comparison of it to a debt, and a debt is not exclusive to a relative.

The most cautious approach is to seek permission from the relative. Fasting on behalf of the deceased should be done based on investigation and strong presumption. If anything extra is done, its reward will reach the deceased, and they will benefit from it.