In my wife's case, her breathing never really stopped, but was incredibly shallow at the end. Although she was totally locked in, with no eye movement possible, her shallow breathing continued, barely discernable.
I found these explanations:
The main respiratory muscles are under both voluntary and involuntary (automatic) control. These two control systems come from separate sites in the CNS and have separate descending pathways.
Neural regulation of respiration. - PubMed - NCBI
The breathing muscles are controlled automatically from the brainstem during normal breathing but can also be controlled voluntarily from the motor cortex.
https://www.neura.edu.au/research/p...ary-and-involuntary-control-human-breathing-1
Humans can breathe automatically (automatic breathing), e.g., during sleep, whereas breathing can be controlled voluntarily when needed (voluntary breathing), such as singing and speech. Automatic breathing is believed to originate in the brain stem via the pontomedullary respiratory oscillator. A descending bulbospinal projection from the oscillator synapses with the spinal cord anterior horn cells with rhythmic projections to the respiratory muscles to cause automatic breathing. The oscillator could function automatically without any peripheral feedback and responds to changes only in pH and Pco2.
In contrast, cortical inputs are required during voluntary breathing. Spinal motor neurons receive corticospinal inputs originating from a discrete region of the motor cortex,
Voluntary Breathing Influences Corticospinal Excitability of Nonrespiratory Finger Muscles
There are three types of muscles: cardiac, smooth, and skeletal.
Cardiac muscles are only in the heart. Skeletal muscles are voluntary. Smooth muscles are automatic (except the diaphragm, which is both voluntary and involuntary.)
Smooth muscles are found in many different locations throughout the body, such as the iris of the eye, the walls of arteries, surrounding the small intestine and stomach. Generally, smooth muscles are also involuntary. An exception to this is the diaphragm, a smooth muscle that regulates breathing, which can be consciously controlled, but generally functions without the individual’s notice. Smooth muscles are not striated. The functions of smooth muscles are as varied as their locations. These muscles regulate blood flow, move food through the digestive system, and even change the angle of hair follicles to maintain body temperature.
Biology Laboratory Manual | Muscles