In Monroe, Louisiana, there are two streets, Edwards Street and Williams Street, that are seemingly disconnected from the rest of the city streets, despite being surrounded by them. A concrete driveway connects Edwards Street to Washington Street.
Aerial: http://goo.gl/maps/BkGFI
Street View from Washington Street: http://goo.gl/maps/Lrcvq (Note that there's only a Washington Street sign blade.)
Street View of Edwards and Williams Street intersection: http://goo.gl/maps/9I2Si (Those street blades must be TBORS material.)
Growing up and driving by this area, I always found it very interesting, almost like a little enclave. Are there any other occurrences like this anywhere else?
Pretty normal when a new road cuts through an outlying section of an older grid.
Historic Aerials gives you a good idea what the streets were like before Washington Street came through:
http://www.historicaerials.com/aerials.php?scale=6.42391693199087E-6&lat=32.5184581890527&lon=-92.0999972277827&year=1969