Search for objects that don't have a property at all, not just empty?

We have migrated some of our old classes to new ones. The one old class had "OldProperty" which is not on the new Classes. The users have decided that they want to populate some "NewProperty" if the object used to be Old Class with a blank OldProperty.

Since Properties, once they have values roll forward with the object, I can search for new class obects that have a value in OldProperty. But, as far as I can tell there is no way for me to search for empty "OldProperty" because it would not exist on the new objects.

Is there any way to do this without formally attaching OldProperty to the new classes?

-Jason