Yes. Your brain controls everything, including the heart, so if the brain stops, then you will forget how to breath.
If your brain completely stops functions, your heart will stop.
However, in many cases the higher functions of the brain fail while the basic housekeeping functions continue to work. In that case you may be in a vegetative state, unable to think or recognize your surroundings, but your brain still tells your heart to beat and your lungs to breath.
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Oh yeah, I agree.