One of the most common cliches to have arisen over the years is the customary "Zzzzz" which is used to represent a sleeping person. It is very hard to see how this originally came into place, as there are very few, if any, people that actually make this noise when they are dozing, unless they are subconsciously attempting to conform to a stereotypical snooze.
It is possible that "Zzzzz" is an attempt to indicate that the relevant person is snoring. This sounds logical until you realise that to make that noise when snoring implies a severe medical problem that should be corrected immediately.
Most probably it is merely an attempt to imply sleep using something with absolutely no connection to sleeping whatsoever, and, one might even suggest, with the real world. This seems the most likely possible explanation.
The conclusion you can draw from this is: if you hear someone making this noise while apparently asleep, they are obviously faking it.