Is it permissible for a person to slaughter a number of animals with the intention of fulfilling the vow of his deceased mother, who had vowed to slaughter a sheep and distribute its meat to the needy many times, and to give some of it to his financially struggling siblings, and what should he do about the debts for which he cannot find the creditors, knowing that she enjoined him to fulfill her vow and pay off her debts?

If the mother has left behind wealth, then any vows and debts she owed must be paid from her estate before its distribution. If someone volunteers to pay them, they have done well. If the vows were obligatory, the heir stands in the place of the deceased in fulfilling them, such as Hajj and other vowed acts, provided the deceased had wealth. If you do not know the exact number of sheep vowed, it is sufficient to slaughter what is most likely to fulfill the vow, because certainty is taken as probability when certainty is unattainable.

It is not permissible to give the vowed sheep to the full siblings or maternal half-siblings from the portion designated for the poor and needy, unless the mother intended that at the time of the vow, or if custom dictates it. Otherwise, it must be given to the needy who are eligible for the mother's charity. The one who made the vow, nor their ascendants or descendants, may eat from the vow designated for the poor, unless the one who made the vow intended to eat from it at the time of the vow, or stipulated it verbally, or if custom dictates it.

As for debts owed to unknown creditors, if you are unable to reach them and have despaired, then give the money in charity on their behalf. If they appear thereafter, give them the choice between endorsing the charity or having the debt returned to them. The reward for the charity will be yours.