Well, it throws the whole process into disarray, as we found when Wellstone was killed, just 3 weeks before the election, and as he had opened up a fairly substantial lead in the polls.

The party had to nominate a new candidate to run in his place, and were only able to do so by squeaking in under the deadline for getting on the ballot by a nose.

So, the simple answer is, it would depend upon when it happened, and no, the runner up wouldn't have a legal right to be put on the federal ballot.

The way Republican Norm Coleman of MN won the senate seat in the wake of Democrat Wellstone's death, was the most perverse dirty tricks campaign I ever witnessed (and I've seen some real dirty shit), and turned me off to conventional politics, probably forever.