It's sometimes held that, though there are no necessary beings, yet it is impossible for there to have been nothing at all. Each possibility is represented by a possible world, and some accounts (e.g. Lewis' identification of worlds with spatio-temporal regions) leave no conceptual room for an empty possible world, so total emptiness is -- according to such accounts -- not a possibility.
I find such reasoning suspicious. It's generally the case that you can (conceptually) substract a contingent entity from the world, and nothing need replace it. The result is still possible. (Another "possible world", if you want to call it that.) This fits nicely with Humean views banning necessary connections between distinct existences, and all that. Not to mention Lewis' own combinatorial principle. So why should this suddenly change when we're down to the last object? Why would its subtraction necessarily require replacement by something else? The suggestion seems awfully ad hoc.
Thinking modally, it seems clear that its substraction does not require replacement. It is merely Lewis' definition of a possible world that leads to his anti-void conclusion. So we find that his account fails to track fundamental modal matters in this respect. (I use Lewis as an example; the same will be true of any account of possible worlds which leaves no room for nothingness.)
We might conceive of possible worlds as representing only intrinsic existences. By this I mean that they don't make claims about anything 'external' to the world itself. On Lewis' picture, for example, worlds are simply spatio-temporally isolated regions -- universes, in other words.
Each possible world may or may not have the additional property of obtaining, or being made concrete or "actual" (in the absolute, non-indexical sense). Our world has this property, for example. We typically assume that no others do. But if worlds are characterized intrinsically, then there's nothing to stop multiple worlds from being actualized. And of course Lewis himself holds that all possible worlds are concrete. But on such a picture, why couldn't it be that none of the worlds are actualized?
This picture is puzzling because it leaves meta-modal facts of 'actualization' unaccounted for. Which worlds get this "special property" is, it seems, no simple first-order fact internal to the worlds themselves. But on the standard view [see below], extra-worldly meta-modal facts are static and necessary. This entails what I call "narrow fatalism".
It might make more sense to instead conceive of worlds as maximal compossibilities, and thus containing within themselves some 'external' or meta-modal facts. Then, for example, the existence of multiple independent spatio-temporal universes would constitute a single possible world. After specifying all of the "intrinsic" or positive facts, the world would need to add an extra claim to the effect of "that's all". For example, our possible world might consist of our universe and that's all. Then it would be impossible for any other universe to be actualized alongside our own, for that would contradict the "that's all" clause.
But then why can't you have a possibility that consists in nothing but the "that's all" clause? It seems perfectly coherent, given our assumption that there are no necessary beings. Insofar as an account of possible worlds rules out this possibility, I'm inclined to think that the account fails to accommodate all the possibilities. For this is surely one of them!
Aside: note that we no longer need to think of 'actualization' as a meta-modal property which attaches to worlds. Instead, we might give a deflationary account, according to which a world is actual just in case the possibility it uniquely describes is realized. In this way, the meta-modal fact can "piggy-back" on the worldly facts. A world's actuality merely consists in its claims all being true.
A final point: we might think that various abstract or 'Platonic' objects exist necessarily. Possible worlds themselves might be an example. Presumably even if nothing (concrete) existed, still our universe would have been possible. That's certainly the case on the standard S5 modal-logical picture, which sees all modal facts as static and necessary. (If p is possible then it is necessary that p is possible. The contingent facts may vary from world to world, but the modal facts are "extra-worldly", concerning a static modal-multiverse which remains unaffected by your world's location within it.)
In that case, the above discussion should be reinterpreted as concerning the question whether there could exist nothing concrete. (Perhaps nothing internal to a world, if we think of worlds as containing the contingent concrete stuff, and Platonic entities as genuinely "other-worldly", i.e. existing outside of worlds.)
We might instead consider a dynamist meta-modal view, according to which even modal facts can vary from world to world. On this view (which is of dubious coherence), some things are metaphysically possible which might not have been. And other things aren't possible, but they could have been possible if things had turned out differently. (They just couldn't have been actual.) So we might try to defend the possibility of total nothingness by suggesting that our necessities might not have been necessary. But note that they still couldn't have failed to exist (since they are actually necessary, after all), so that doesn't help after all. At best, a totally empty world might be possibly possible, but not actually possible, if we accept that some things are contingently necessary. But this is getting messy and borderline nonsensical, so I'll leave it at that.