Our Gemara on Amud Aleph discusses the idea that there is a degree of responsibility for a child to pay his deceased parent’s debts. The poskim analyzes the nature and basis of this obligation, which also suggest ideas about the limits and obligations of the commandment to honor one’s parents. This obligation is beyond a financial lien, such as if the parent did not leave real estate (in the times of the Gemara, non-real estate holdings that were inherited or sold, i .e. chattel, was never subject to a lien.) So even though the creditor could not extract payment via an act of legal repossession, the child is still obligated through force of a mitzvah to try to make restitution.
One question in the poskim arises regarding if the parent left no assets at all. Some argue that since a child is only obligated to honor his parents using their funds and not his own, here he would be exempt. Others argue that even though that is technically true, it is still recommended to perform the mitzvah of honoring parents even with one’s own funds, if necessary. In addition, some argue that when there is a matter of disgrace and not merely wishes or requests, the obligation is in force even without funds. Since not repaying debt is dishonorable, the child must do what he can to redeem his father’s honor. All the more so if the father was negligent in not paying his debts, thereby making it important for the son to redeem his soul. (See Rambam Mamerim 6:10, Shu”t Chasam Sofer CM 177, Aruch Hashulchan CM 107:2.)
Up to this point, we are discussing the halakhic technicalities, and in essence how this is one final way for a child to honor a parent. It is also important to reflect on the powerful beneath-the-surface emotional processes for the child as well. In many situations there is an strife and familial discord when it comes to inheritances. A large portion of civil court and Jewish court cases are in regard to arguments about the estates. I do not believe this is simple greed. Indeed, certain family disputes transcend rationality, and are not really about money at all. Rather, for many people, the inheritance is the final act of love that the parent does for the child. There can be an enormous amount of meaning attached to various objects in the estate, including money. All the more so if the attachment to the parent was not ideal, then the only place for the love to be symbolically represented is in the leftover estate. The estate can be experienced as one last attempt to heal an unrequited wish for recognition and love from parent to child.
Ironically, this might be the true unpaid debt of the father.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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