How many hands do you have? Two? Or do you havethree? Your left hand, your right hand, and the non-existent third handthat's attached to your head? Obviously, that last "hand" shouldn'tcount. To say that you don't have a third hand isn't to say that youhave a hand that possesses the particularly stunting property ofnon-existence. We get ourselves into a real muddle if we take claims ofnon-existence to mean that there is some object that has the propertyof non-existence; for then that object must both exist (to have anyproperties) and not exist, and that can't be. So when we say that noone came to the party, we mean to deny that someone came to the party — not to affirm that at least one person did, namely "no one", the"non-person", the person with the rather anti-social property of non-existence.
This confusion becomes unavoidable if one assumesthat every noun in a language must refer to something. For if youassume that, then when you come upon a sentence like "Nothing beats aroyal flush" you'll be forced to conclude that something does after allbeat a royal flush, namely Nothing. This assumption is mistaken. Notall nouns contribute to the meaning of sentences in the same way. Inparticular, some (like "nothing") don't refer to anything while others(like "Manhattan") do.
So, to turn to your question, it's aconfusion to think of Non-Being as something that's jockeying Being forthe same space. In any given space, either there's something orthere isn't. And if there isn't anything there, if there's nothingthere, that doesn't mean that there's actually something there, namelyNon-Being.