An interesting take on this is depicted in Attack on Titan, where they do in fact wall all the fields - the city (I don't remember if it's like the last vestige of humanity or whatever) is surrounded in concentric ring walls, the outer one which contains villages and farmland having a circumference of about 3000 kilometers for an internal area of 723,822 km², making its area just a bit smaller than Zambia and Chile.
Of course, a 3000 kilometer, 50 meter tall wall is ridiculous. But then again the great wall of China is 21.000 kilometers long. I believe there's more info about the walls and their construction in the source.