Your debts get paid out of your estate. If there are not enough assets in the estate then the estate can go bankrupt - creditors get nothing, or share in whats assets are left. Just like if you were to go bankrupt while alive.
Rolf, Life insurance wouldn't be available to creditors. There is section in the life insurance legislation which prevents this.
So, a potential strategy could be to use trusts to invest (with no loans to the trusts from yourself). Be impercunious. Get huge life insurance policy and crank up hte credit cards before you die.