Theoretically, it might be possible, but in reality it isn't.
Basically, how candidates get on the ballot is a matter of state law. For the general election for president, most states automatically give "established parties" a ballot slot on the general election ballot. That slot goes to the nominee of the national party as chosen at that party's national convention. Besides the established parties (the Democrats and the Republicans in every state and the Libertarians, Greens, and Constitutionals in a significant number of states), other parties and independents can attempt to petition onto the ballot (which takes a certain number of signatures). Thus, nationally, there are actually a large number of "remaining" candidates at the general election, not just two candidates. The rules, however, usually assure that there is only one Democrat and one Republican on the general election ballot.
There are two ways that a party could get two candidates running for President in different states on the general election ballot. First, if a party is not an established party in the state, the people putting a slate of candidates together for that party in that state do not have to choose the same presidential candidate as the national party. Second, while most state laws are clear about the initial presidential candidate for an established party, they are less than clear about what happens if that candidate dies or withdraws before the general election. Thus, it is possible that some state parties might choose a different replacement candidate than the national party suggests. (Given different time frames in different states for picking a replacement candidate, some state parties might have to pick their candidate before the national party meets to pick a new candidate and be unable to change later.)
Additionally, the candidates on the general election ballot are legally only placeholders for a slate of electors. Normally, 99% of the electors vote for their party's nominee. But if something happened to the party's nominee after the election, there are no rules governing how those electors would actually vote. Undoubtedly, the national party would try to suggest whom those electors should vote for, but the electors do not have to follow that suggestion. If the party with the deceased candidate won the electoral college by a landslide (say 450 or more electoral votes), the split of electoral votes might result in three candidates from that party having more electoral votes than the candidate of the other party -- meaning that one party would have the final three candidates when the House picked the winner of the election. (An election has only gone to the House on two occasions -- 1800 and 1824.)