Neither the legal guardian (walī) of the deceased nor any other person may fast in place of one who has passed away in order to make up the fasts that remained unfulfilled. This is because fasting is a purely bodily act of worship (ʿibādah badanīyah). Such acts must be performed personally by the individual concerned; deputation (niyābah) in bodily acts of worship is not permissible. The sole exception to this principle is pilgrimage (ḥajj), in which deputation is allowed under certain conditions.
Accordingly, the proper course of action is not to undertake fasting on behalf of the deceased, but rather to discharge the fidyah due for the fasts that he or she was unable to observe.