Whoever dies and he owed an obligatory prayer, or prayers, he is not under any compulsion to make them up. This is because the origin of acts of worship is not to penalize the mandatory acts, and nothing is exempted from this origin, apart from what is mentioned in the law on the penalty for persecution on them, for example: Hajj, Obligatory Fasting and Zakat.

As for obligatory prayers, there is no evidence for allowing penalty for it, and is not right to apply the analogy for hajj on this, because it is an act of worship. Analogy in acts of worship is not acceptable.

In the writings of Imam Malik bin Anas, that Ibn Umar RA told him: “No one fasts for another person, and no one prays for another person”. It is suggested by ibn Umar that even if he is Non muslim for fasting, due to the specific evidence on this matter, except that he is muslim in the matter of prayer.

Therefore, whoever’s father has passed away and he missed some obligatory prayers, whether he missed them when he was ill, or when he was healthy, there is no compulsion on him to make them up. It is the child’s duty to make dua (supplication) and ask forgiveness for his father for missing them, ensuring his will is implicated after his death, honoring his friend, and strengthening the ties with those he has no ties with. 

And the best thing a son can do for his deceased parents is to make dua’ for them, or voluntary charity on their behalf (like endowments) due to the narration of the sahih hadith on this.

As for Zakat, it is still obligatory on the deceased if he did not pay it before his death, because it is a financial right that he owns, Ibn Muflih said in “Al furu’:

Zakat doesn’t stop being obligatory upon death, and it is taken from the stipulated wealth that the deceased had left behind, and if he hasn’t stipulated for example a tenth, if he has, then it is taken from his third according to Abu Hanifa and Imam Malik.

As for fasting, the scholars have agreed that no one can fast on behalf of another person, and if he fasts on behalf of another person it doesn’t benefit that person, and the obligation still remains.

However, there is some difference in opinion regarding fasting for a dead person. Most of the scholars have agreed that it is permissible to feed a person on the behalf of one who has died and had missed an obligatory fast without a valid reason/excuse. As for the person who dies without fasting for a reason then there is no wrong on him, the fast is no longer obligatory on him, and it is said it is liked that one should fast on behalf of such a person.

Imam An-Nawawi and Al Shafi’ -May Allah have mercy on them- said in explanation of Muslim:

The scholars have differed in opinion on the issue of one who has passed away and he had obligatory fast from ramadan to make up. Should one fast on his behalf? Al shafi’ has two famous sayings on this matter. The most famous is that no one should fast on his behalf and it is not correct to fast on behalf of a dead person in the first place. The second famous saying is that it is liked that his guardian should fast on his behalf. The guardian should make his fast correct and the deceased’s debt is waived and he doesn’t need to feed anyone on his behalf.

What Muslim means by “whoever dies and he had to fast some days, his guardian should fast on his behalf” and the well known hadith; “whoever dies and he has upon him a fast, people should be fed on his behalf”, is not a solid ruling. If it were a solid ruling, then it would have been possible to join between these two hadiths, and that both acts are permissible. Hence, whoever had fasts to make up it is permissible for the guardian to feed people on his behalf, and it is correct in both cases. That is, where one fasts on behalf of the deceased and it is also permissible to feed people on behalf of the deceased, and the guardian can choose between the two options. 

This is a summary of the question and what the salaf, tawus, Al Hasan Al Basri, al Zahri, Qatada, Abu Thawr, Al Layth, Ahmad, Ishaq and Abu Ubaydah, have to say on fasting based on a promise outside of ramadan. 

The majority are of the opinion that one cannot fast on behalf of a person whether a promise is made or not. Ibn al Mundhir said of Ibn Umar, Ibn Abbas and Aaisha and narrated of AL Hasan, Al Zahri and Malik said and Abu Hanifa said, judge Ayad said that it is the view of majority of the scholars. They gave importance to the hadith on the guardian feeding people on behalf of the deceased and this is a weak narration, and it is incorrect and any necessity for it and any hindrance prevents it from working outwardly with the pretense of hadiths without contradicting them.

It is said in “Al Majmu” :

As for the scholars of the schools of thought on the question of a person who had fasts to make up and has now passed away, either due to an illness, or travelling or other reasons, and he was unable to make them up until he died. The shafi’ school of thought says there is nothing upon that person, and there is no need to fast on that person’s behalf or feed people on his behalf. They have no dispute in this opinion.

And in this school of thought Abu Hanifa and Malik and the Majority have said: 

Al Abdari said: and it is the saying of all of the scholars apart from Tawus and Qatadah they said: They must feed people on behalf of the deceased everyday a poor person, because he is weak and like an old man. 

Al Bayhaqi and others opposed the people of the Shafi’ school of thought, by quoting the hadith of Abu Hurayra that the Prophet said: (And If I order you to do something, then do of it as much as you can) narrated by Al Bukhari and Muslim. They also gave evidence of the analogy of hajj as mentioned in the compilation, and they differed over this and the old man, according to Sheikh Amir Al dhimma and is from the people of worship on behalf of the deceased.

And Al Shirazi a known scholar of fiqh from the Shafi’ school of thought said: 

If he had upon him some fasts to make up from Ramadan, and he did not make them up and he died, and if he delayed them for a reason and then died- then there is no obligation on him. This is because it is an obligatory act which only death can prevent him from doing, so the obligation is no longer upon him like that of Hajj.

And ibn Qudama Al Hanbali said in al Mughni:

Whoever dies and he had some fasts to make up from ramadan, then he is only free from them in two instances:

One of them, is he dies before he is able to fast, either due to time constraints, or a valid reason such as sickness or travel, or inability to fast due to weakness, then for this there is nothing on him, as per the saying of a lot of the people of knowledge, and the saying of Tawuws aand Qutada that they said: it is obligatory to feed people on his behalf, because obligatory fasting was lost on him due to his weakness and inability to complete the, so it is obligatory to feed people on his behalf, like an old man who did not fast because he was too weak and unable to do so.

The evidence given by the majority is that it is Allah’s SWA right  and an obligatory by law. If someone dies before he is able to fulfill this obligation then it is no longer upon him, like Hajj. It differs from an old man, as it is still obligatory upon him, unlike the deceased 

The second situation: He dies after being able to make up the fast, then it is compulsory to feed a poor person on his behalf for every day he missed. This is the saying of the majority of the people of knowledge.

If the sick person or traveler dies while in the state of sickness or travel, then it is not an obligation to make up the fasts missed, because such have not satisfied the conditions for making them up on other days. If the sick person is cured and the traveler becomes a resident, and they died, then there is an obligation to make up the fasts as the conditions of health and residency have been fulfilled so they could have made them up on other days. The meaning of obligation here is that it has become possible for him to make up the fasts, and he is exempted from this responsibility in two cases:

1. Either his guardian fast on his behalf, due to the hadith of Aisha RA in the two sahihs: “ whoever dies and upon him was a fast, his guardian should fast on his behalf”  (agreed upon AL Lu’lu’ wa Al Marjan 704) Narrated by Al Bazar and he added a word “ If he wished” (Said in the compilation of extras 179/3 and its chain is hasan).

The fasting of a guardian on behalf of the deceased is from his love and righteoussness but there is no obligation on him to do so. This is supported by the narrations of the Sheikhs: Ibn Abbas: A man came to the Prophet and he said : Oh Messenger of Allah, my mother has died and she had one months fast due on her, do I fulfill them on her behalf? He said : Yes, the debt due to Allah is the one which most deserves to be paid. (AL Lu’lu’ wa Al Marjan 705)

It is known that a person is not under any compulsion to give the debt of another person except from his own righteousness and love, as the basis is to waive the responsibility. The person waiving the responsibility has no obligation on him to perform what is the responsibility of another person. The correct is that fasting on behalf of the deceased is allowed, but there is no obligation. If he done, the deceased is freed from his obligation.

2.By feeding people on his behalf, that is, giving food to poor people from the deceased wealth which was left behind, for everyday he missed because the debt is for Allah and is linked to his wealth that was left behind, and the debt of Allah is is the one which most deserves to be paid 

And some of the scholars have set the conditions that the person must have asked for this to be done in his will, and if he didnt, then nothing is taken from the wealth he left behind as this is the right of his heirs.