You're thinking of Mel Carnahan, whose wife, Jean, got the seat.
"Carnahan served as Missouri's First Lady for nearly eight years. Just three weeks before the November 2000 election, her husband, Governor Mel Carnahan - while campaigning for the United States Senate - was killed in a tragic plane crash along with their oldest son, Randy, and long-time advisor Chris Sifford.
"With her husband's name still on the ballot, she agreed to serve in his place should he be elected, which he was with a 48,000-vote margin of victory.
"Jean Carnahan was sworn into to the Senate on January 3, 2001, becoming the first woman in Missouri history to serve in the Senate."
http://carnahan.senate.gov/Bio.html
Note that when people were voting for Mel, they knew they were really voting for Jean.
Different states have different laws. My understanding with Minnesota law is that they could do that (leave Wellstone's name on the ballot), and then Gov. Jesse (The Body) Ventura could appoint whomever he chose to serve Wellstone's term. (I saw differing things on that, though -- may be that in Minnesota his name _can't_ be on the ballot since he died.) It looks like they are going for supplemental ballots and Walter Mondale as the candidate.