The brain stem is largely responsible for autonomic, survival-related functions like breathing. The medulla oblongata and the pons, located in the brainstem, regulate breathing and breathing rate automatically, by sending nervous impulses to related structures (diaphragm and intercostal muscles) for inhalation and exhalation.
When Amy (Andrea’s sister) died and turned into a Walker, she appeared to take a breath. This would actually happen, as there was no apparent damage to her thoracic area. It can be assumed that, since motor and sensory impulses could be sent throughout a zombie’s body (making them move, able to hear, etc), then autonomic impulses such as those for breathing would also be sent out.
