Resonance structures don't really 'exist' as drawn. Resonance structures are contributors to the actual molecule. Meaning that any given molecule for which valid resonance structures can be drawn is actually a hybrid of those resonance structures. The degree to which a given resonance structure contributes to the actual structure depends on the likelihood of that particular resonance structure existing at any given point (or more clearly the stability of that particular resonance structure).
The structure you have drawn with the double negative charge would be highly unstable and so is not likely to contribute very much to the actual structure of the molecule. That doesn't mean the resonance structure is invalid, it's just not significant.