Even if Missouri law didn’t specify that a U.S. Senator must be a resident of the state on Election Day, Article I of the U.S. Constitution sets such requirement. But it is simply false to claim that when an unqualified candidate finishes first in an election that the second-place finisher is entitled to the seat. There have been a lot of candidates who have won an election posthumously, and in every case that I’ve seen it has resulted not in the second-place finisher winning, but in a vacancy (within the past half century, it happened after the deaths of Congressmen Hale Boggs, Nick Begich and Patsy Mink, and it also occurred several times previously, plus in many non-congressional elections). So the Widder Carnahan was not appointed illegally or unconstitutionally.
We have the same specification in Tennessee. If you die immediately before the election, your name is stricken from the ballot, period. Now, a particular individual recognized that and murdered his State Senator opponent. Only because it was found out immediately and a quick, bipartisan effort to write in the widow’s name saved the seat. This was the legal way to do it, but I vigorously disagree in the case of Missouri: Mel Carnahan was dead, and therefore must be stricken from the ballot. He was no longer a legal resident of the state, period. A write-in candidacy was the only legal and ethical manner in which for Jean Carnahan to have assumed the seat. There was also the added concern of voter fraud surrounding the election in Missouri, which cost not only Ashcroft his seat, but Jim Talent the Governorship. All of that should’ve been enough to deny seating Mrs. Carnahan.