The issues regarding the exact disposition of any unclaimed property will depend upon the specific nature of that unclaimed property. Abandoned property of a personal nature, for example, follows an entirely different set of rules than unclaimed property of a real estate nature. In general, unclaimed property of a personal nature may be in some capacity granted to the finder of that unclaimed or abandoned property, while in real estate, this is generally not the case.
In real estate law, a concept called escheatment exists. The idea of escheatment is that unclaimed or abandoned property can revert to government control and ownership in certain circumstances, particularly so as to avoid issues with such property being held by no particular individual.
Because real estate is a constant type of property, and because if it were unclaimed property there might arise any number of issues regarding how exactly to claim it, the legal system is set up to deal with these problems primarily by simply granting this unclaimed or abandoned property into government custody, where an individual might be able to obtain it.
Of course, normally, the rules regarding such abandoned or unclaimed property allow for the real property owner to come forward and reclaim the property within a certain time frame and a particular set of circumstances, as ultimately, much of the law regarding unclaimed or abandoned property in America is designed to ensure that the original owner will eventually be able to reclaim that property.