Is the estate to be distributed among the heirs if it is insufficient to settle the deceased's debts, or even half of them?

Nothing from the inheritance should be distributed to the heirs before all the deceased's debts are paid. If anything remains, the heirs take it; otherwise, not. This is because the payment of debt takes precedence over the rights of the heirs, as Allah the Almighty says: ﴿from after any will he may have made or any debt﴾. The debt of a human being is obligatory to be paid, according to Islamic law, before the distribution of the inheritance, so that the deceased's liability is cleared. If what the deceased left behind is not enough to cover all his debts, then the existing assets are distributed among the creditors proportionally.