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I suppose when the robot footprint enter the obstacle region, the navigation stack should stop the robot to prevent collision but it didn't happen. Why?

No, that is the CENTER of the robot that must not enter the lethal costmap (colored in cyan). If you have an asymmetric footprint, the cyan region you see in the first image is the obstacles + inscribed region (which is the smallest distance from the robot's center to the footprint). If the center of the robot is inside the lethal region, it is certainly in collision.

Then there is the circumscribed region, which would envelope your whole footprint and that may or may not be in collision, depending on the orientation of your robot.

Check this image for better understanding (from http://wiki.ros.org/costmap_2d):

image description