If a special election was held, they would immediately contest Stephenson's residency and prevail since she clearly did not meet the law's requirements.
Are you saying she's the only Republican in that District? There is no other candidate that could run? In a case like this the Kentucky Republicans are in a great position to solidify the seat and put an end to the controversy by running an appealing candidate with no residency doubts who will in a special.
This problem should have been caught when she filed to run for election, not days before the voting. Once again, we pay someone to do a job that they can't be bothered doing.