At the end of the series, the Governor of New York State appoints Maude to the House of Representatives, filling a vacancy caused by the death of her local Congresswoman. In fact, vacancies in the House of Representatives caused by the death, resignation, or expulsion of a member can be filled only by a special or general election. The rules for filling vacancies in the U.S. Senate, however, vary from state to state.
On Maude's first appearance on All in the Family (1971), it was stated that all three of her previous husbands had died during their marriage (one of them on their honeymoon). On this series, however, it's repeatedly stated that only her first husband had died; she had divorced the others.