When someone is dying a natural death, there is a breathing pattern that usually happens. It goes something like this: a deep breath or two, then holding it, followed by a shallow breath or two, and so on. It is an uneven pattern of inhales and exhales. It can be scary if you don't know it is coming.
Another thing that happens as the person gets closer to death is that the time between inhales widens. When breaths are towards 20-30 seconds apart, death may be happening very soon. I say "may" because there is always someone who has this breathing pattern and will live much longer. Overall, breaths will be getting more shallow and the time between inhales will space out.
There are exceptions to everything, but generally this is what you will see. Of course right now I want to tell you all the ways it could be different and how many different ways breathing can look even with the above very general guidelines. But, the best thing to do when you are going through this time is to ask your hospice doctor or nurse about what to expect. I do this with the people I care for by showing them some of the ways it can look and so when it happens, they aren't as startled.
The pattern is called 'cheyne-stokes' respirations:
"...Cheyne-Stokes respirations refer to a rhythmic change in respirations wherein breathing becomes shallower and shallower variably with a slowing in respiratory rate that culminates usually in complete cessation of breathing for several seconds to more than a minute. This is followed by progressively stronger respirations that become exaggerated and quite deep. This pattern is thought to result from abnormal brainstem responses to CO2 levels in the blood - initially undercompensating and then overcompensating. Cheyne-Stokes respirations can occur in other nonterminal disorders such as heart failure and stroke. It is interesting to note that patients who are able to speak generally say that no distress is associated with this breathing pattern. From this we may extrapolate to dying patients, who usually cannot speak with Cheyne-Stokes respirations, and presume that the syndrome is not disturbing to the patient. However, family members and clinicians may assume or project distress into this syndrome and thus often need to be coached. I usually explain that the pattern results from a breakdown in "cycling" between the lungs and the brain and that, as far as we know, it is not bothersome to the patient..."
~Palliative Care Perspectives – James L. Hallenbeck, MD