Full Idea
A Fregean about existence claims would say that 'that hobbits do not exist' is nothing other than the claim that 'being a hobbit' is not exemplified.
Gist of Idea
Fregeans say 'hobbits do not exist' is just 'being a hobbit' is not exemplified
Source
Trenton Merricks (Truth and Ontology [2007], 3.II)
Book Reference
Merricks,Trenton: 'Truth and Ontology' [OUP 2007], p.43
A Reaction
'My passport has ceased to exist' seems to be a bit more dramatic than a relationship with a concept.