Gee, I hate to ruin this with the actual answer, but it's this:

The party picks who will be its candidate. The vice presidential pick is not automatically elevated to this position unless the party rules say so (and they don't). The party would re-convene its convention (perhaps electronically) and take a new vote. Delegates were only obligated to vote for their state's primary or caucus winner on the first ballot, so in this reformulated convention they could vote for anyone that meets the party's rules.

The electoral college decides who will be president. If the candidate dies but is still on the ballot (dies too close to the election or dies after the election), the electoral college decides who wins - and it is not automatically the runner-up or the vice presidential pick.

Of course, if the president dies after being sworn in, the matter is more straightforward because there is a constitutional line of succession. This is the first time that the vice presidential pick ends up with a formal claim to the throne, so to speak.