Meinongianism Claim: Existence is a property that some objects possess and some don't; there "are" non-actual or non-existent objects (such as Santa Clause, possible worlds, and perhaps even impossible worlds).
Question: What would then be the difference between a non-existent object and an abstract object, such as a proposition or the number 2?
The difference is simple, non-existent objects don't exist whereas abstract objects might.
For example, round squares are non-existent because they are self-contradictory. The golden mountain is non-existent because it is not actual. Fictional entities are non-existent because fiction isn't literal truth.
Non-existent objects are not (at least, needn't be) abstract. The golden mountain really is made of gold, it is concrete and not abstract--- it just doesn't exist. Likewise, there is a detective who really lived at 221b Baker street, he just didn't exist.
Meinongianism and the theory of non-existent objects has not gotten wide acceptance. Most philosophers who advance some sort of Meinongianism these days try to accomplish the same as the distinction between exist/not-exist with some other distinction(s) like abstract/concrete or actual/possible/impossible.
See this article, especially section 5.4 for more discussion of this.
For Meinong, abstract objects that have being, but aren't in space or time, subsist, or exist, just non-spatiotemporally. He took mathematical objects to exist there; presumably this is the modality of being of the sort Quine would take sets to occupy, and the same goes for Frege and Gödel. Impossible objects and fictional objects, meanwhile, or things that don't exist either in spacetime or outside of it, but rather don't exist in any sense except for as a set of criteria (or [non-]existence conditions to be satisfied, though again, whether they actually can or cannot be satisfied is another issue, since Harry Potter could exist whereas a round square could not, but both absist).
