Is the failure to document a debt considered a sin for which one will be held accountable, and what if the debt is not repaid after the death of both the lender and the borrower? Does responsibility fall upon the lender for not documenting the debt?

Allah commanded the writing of debt in the verse: (O you who have believed, when you contract a debt for a specified term, write it down). This command is on the basis of recommendation, not obligation. Thus, whoever leaves the writing of the debt does not sin. It is preferable for a Muslim to write down the debt to preserve rights, and there is no consideration for customs that contradict the Book of Allah and lead to the loss of rights. There is no sin or blame in not writing down the debt, but if your sister's husband or his heirs do not repay the debt, then the sin is on your relative, unless you absolve him of the debt.