Recently the High Court of Australia found four senators and one member of the House of Representatives were not properly (invalidly) elected to the Australian Parliament. When they were elected, each was both a citizen of Australia and another country. Section 44 of the Australian Constitution says that members of Parliament can only be a citizen of Australia. The five members of parliament were removed from their positions and the seats were declared vacant.
These five former members of parliament could choose to stand for election again if they were no longer dual citizens. The fact that they have been found to be not validly elected in the past does not stop them from standing again.