It is my understanding that the estate or the trust is responsible unless relieved of that responsibility in some way either through legal means or disposition of the asset in some way. I don't believe an estate can be considered closed unless this happens. I have been told that for certain items, including timeshares, it's not uncommon for the courts to remove items from the estate after a sufficient time has passed with good faith efforts to dispose of the item. I've seen the timeframe of a year mentioned at times in such matters If there are no assets one can just let the estate wither, I've seen that play out first hand. The trustee or executor could not distribute assets "legally" when there are liabilities without satisfying those in some way.I am not sure what you mean about public notice. In an estate or in a trust, someone still has a responsibility to dispose of the asset or item. That doesn't change. A will is also not a legal entity, it doesn't hold anything. What is left after someone passes becomes part of their estate. Not really any different than a trust, except items in a trust are easier to transfer without the need of probate. They all still require disposition.