Is the wife absolved of responsibility for her deceased husband's debts if his brother disposes of his estate and refuses to settle them, knowing that the estate has not been legally distributed and the husband's parents are still alive?

You are not sinful for what happened; rather, the sin is on whoever prevents the repayment of your husband's debts from his estate and disposes of what he does not own. It is advised to take the matter to court to settle the debts and distribute the inheritance among its rightful heirs, and to prevent the husband's brother from disposing of it, knowing that he inherits nothing if there are male children or a father.