Suppose that trope theory is correct. Then what it is for x to have a given property P is to have a trope, say Px, associated with it. But suppose now that x is a reducible entity—one facts about which reduce to the existence and functioning of other entities (e.g., x might be a table—table-facts reduce to facts about particles and societies). In that case, it is surely not the case that what it is for x to have P is for x to have associated with it Px. For if x has Px associated with it, then x is no longer reducible. For consider the fact that x has P. For this fact is the same as the fact that x is associated with Px. But that x is associated with Px does not reduce to facts about how, say, the components of x are arranged. For the latter facts are constituted by association with certain tropes of the components; but the fact we are interested in involves Px. The only way x's having P could reduce would be if facts about the existence of Px somehow reduced to facts about other things. But then Px wouldn't really be a trope. The point of tropes is that they are ontologically basic—facts about them don't reduce.
Therefore, if trope theory is correct, then it does not apply to cases where we predicate something of a reducible entity. This, I think, gives one good reason to say that the reducible entity does not really exist in the same sense of "exist" that the other entities do. After all, if predication means something different in its case from what what it means in the other cases, it seems plausible its entitihood is not univocal with theirs.
I ssupect that the same argument might work with other theories of predication as well. If so, then reducible entities don't really exist in the full sense of the word.