What happens if...

[Niles Caulder]

Going with the hypothetical, and assuming inelligble candidates got on the ballot and 'won,' I'd say it's a bureaucratic issue to resolve--the Office of Voter Registration or whatever have you in the state would issue a statement that the candidate was inelligble, and therefore certify the candidate with the next highest support as the winner.  People could sue if they wanted to, but it would be a waste of time.