Is it permissible for one of my deceased father's creditors to refuse to accept payment of his debt and absolve my father of it, knowing that we are sharing in the repayment of his debts?

What the man did by forgiving the debt of the indigent debtor is commendable, because Allah has encouraged forgiving the debt of the indigent, saying: "And if there is any [debtor] in hardship, then [let there be postponement] until [a time of] ease. But if you remit [it by way of charity], it is better for you, if you only know." And the Prophet, peace and blessings be upon him, said: "Whoever gives respite to one in straitened circumstances or absolves him, Allah will shade him in His shade." Since the rightful claimant has relinquished his right, your father's liability has been cleared.