Full Idea
In the Kripkean perspective, rigidity is understood in such a way that an expression may have as referent at a world an object which does not exist at that world.
Gist of Idea
A rigid expression may refer at a world to an object not existing in that world
Source
report of Saul A. Kripke (Naming and Necessity lectures [1970]) by Mark Sainsbury - The Essence of Reference 18.6
Book Reference
'Oxford Handbook of Philosophy of Language', ed/tr. Lepore,E/Smith,B [OUP 2008], p.416
A Reaction
This means that 'the present King of France' is a rigid designator.