Notwithstanding the general rule that the statute of limitations for recovery of the use and possession of realty may not be invoked against the City, whenever a street or alley, or any part thereof, laid out and shown on the recorded plat of the City has not been opened to public use and has been enclosed with a fence by the owners of the lots lying adjacent thereto, and has remained in the open, uninterrupted use, adverse possession and occupancy of such owners for the period of twenty-one years provided such street, alley or lot is a part of the tract laid out by the original proprietors, the public rights in such street or alley shall be extinguished.