Zoning laws in the US don't govern anything other than the initial certificate of occupancy in most US states. They are irrelevant for subsequent sales.
Like the US, Greece has many properties which would be illegal to build from scratch under existing zoning laws. Unlike the US, Greece has pushed a law requiring that all properties be certified as "having no illegal constructions" prior to sale.
I'm trying to imagine the crisis you would get if you enforced zoning laws against secondary sales in the US. At the very least, all of Boston would be uninhabitable.
In order to sell (in Italy) the building must have the same plan (roofs, doors, windows, walls, ...) that was declared when it was built first. You can pay a fine if there are differences, but only if the actual plan obeys the zoning laws now and would have obeyed them at the time the certificate of occupancy was last released.