1. A vehicle side and rear monitoring system with a fail-safe function, comprising: first connection units including imaging device controllers connected to side-view imaging devices of a vehicle, the imaging device controllers display a side-view image captured by the side-view imaging devices on side-view monitors disposed at a side within the vehicle; and a second connection unit including a controller connected to an around view monitoring (AVM) imaging device, the controller displays an around-view image captured by the AVM imaging device on an AVM monitor located within the vehicle, wherein the controller determines whether an abnormality occurs in the first connection units, displays the side-view image captured by the AVM imaging device captured through the second connection unit on the side-view monitors when the abnormality occurs in the first connection units, and performs an image rotation transformation after distortion of the image captured by the AVM imaging device is corrected to be identical with the image captured by the side-view imaging devices when the image is displayed on the side-view monitors through the second connection unit.