To whom and how can I pay the debt I owe my deceased aunt, who has no husband or children, and whose siblings' or their children's whereabouts I do not know?

If a woman has no inheriting ascendants or descendants, nor full, paternal, or maternal siblings, then her brothers' sons inherit her entire estate by ta'sib (residuary inheritance), based on the Prophet's (PBUH) saying: "Give the prescribed shares to those entitled to them, and whatever remains is for the closest male heir." And the deceased woman's nephew is considered among the heirs.

Therefore, the debt he owes her is considered part of the estate, and he is entitled to his legal share from it. The remainder goes to the other sons of the deceased's brothers, and he must search for them and deliver their share to them. The money remains with him as a trust until he finds them.

If, after searching and diligent effort, it proves impossible to find them, he may donate it as charity on their behalf. If the heirs appear later, they are given the choice between confirming the charity or reclaiming their money. He will still receive the reward for the charity.