From what I've collected, Quine seemed to have solved the problem of non-being by using Russell's theory of definite descriptions through the negation of the x having certain properties/descriptions. However, I hear Kripke rejected Russell's definite descriptions. How did Kripke solve the problem of non-being with his theory of reference?
Kripke has more recently come to hold that socalled fictional entities are real entities, and more specifically Kripke holds that e.g. Scherlock Holmes is an abstract object created by the author A.C. Doyle. This strategy may solve many riddles concerning socalled empty names, and perhaps create new riddles.
Kripke, Saul A. 2011. “Vacuous Names and Fictional Entities.” In Philosophical Troubles: Collected Papers, Vol. 1, 52–74. New York: Oxford University Press.