Full Idea
Unlike standard first-order logic, free logic can allow empty names, but still has to deny existence by either representing it as a predicate, or invoke some dubious distinction such as between existence and being.
Gist of Idea
Free logic at least allows empty names, but struggles to express non-existence
Source
Kent Bach (What Does It Take to Refer? [2006], 22.2 L1)
Book Reference
'Oxford Handbook of Philosophy of Language', ed/tr. Lepore,E/Smith,B [OUP 2008], p.538