When talking about either insolvent or bankrupt estates, I often hear people comment that nobody needs to do anything about it because obviously there are no assets. But that's not necessarily true. A deceased person could have a half-million dollar home and another half-million in investments, but if he or she has more than a million dollars in debts and liabilities, there isn't going to be enough money to pay all the creditors. So even though there are assets, the estate is still insolvent. And someone still has to sell that house and cash in those investments on behalf of the deceased person and pay out the proceeds.
That person is the executor named in the Will. If there is no Will, there should be an administrator appointed by the court in the usual way.
Usually in an insolvent estate, the executor will negotiate with the creditors to come to an agreement as to how much each will get. Often everyone agrees to a certain amount "on the dollar" so that they'll each recover at least part of the debt. It's to everyone's advantage not to turn it into a lawsuit, because fighting it out in court means the resources of the estate, which are already not enough, will end up being spent on legal fees and court fees.
If after an executor starts working on the insolvent estate, it is petitioned into bankruptcy by the creditors or the executor declares that the estate is bankrupt, the executor will have to step out of the picture. The control of the assets and debts will be handed over to the Trustee in Bankruptcy to deal with. The executor's claim for compensation can be added to the other claims against the estate.