What is the ruling on disposing of the estate of a deceased father who was burdened with debts, knowing that the value of the debts exceeds the value of the estate, and that the creditors refuse a settlement? Is it permissible for us to dispose of this money to buy an apartment, or to marry off siblings, or to spend from it on ourselves?

If people claim to have a debt owed to them by the deceased, evidenced by checks, then a check is considered a debt instrument and can serve as proof. This matter is referred to the judiciary for resolution. If the claimants prove their right, then the debt takes precedence over the heirs' right to the inheritance, based on the Almighty's saying: "{... after a will has been executed or a debt paid...}" (An-Nisa: 11). If the debt consumes the entire estate, then the heirs receive nothing. If the debt is greater than the estate, then the creditors divide the estate among themselves proportionally to each one's debt.