On April 21, the Indiana Senate passed HB 1242. Current law says if a general election winner is found ineligible, the runner-up takes the position. The bill changes that, for state office (other than Governor, Lieutenant Governor, and judicial posts) so that if the winner is found ineligible, the position is deemed vacant and the Governor may appoint someone. Indiana has a Republican Governor, Mitch Daniels. See this story.
Most observers expect the current Republican Secretary of State, Charlie White, to be found ineligible. He was elected in November 2, 2010, but he had registered in a precinct in which he didn’t live, and then he voted in that precinct.