In the hypothetical that Biden kicks the bucket, how would the DNC nominate the next presidental candidate? By fiat?
It all depends on what stage of the election cycle he dies in.
Scenario no. 1:
If he were to do right now, before the convention, all the Biden delegates still go to the convention pledged to Biden. Technically they take the vote and, well, oops we can't nominate a dead man. (They could skip this step, nobody would cry foul, but according to the DNC bylaws no delegates are unbound until after the first vote,. Not even the Superdelegates.) So it goes to a second round with all the Biden delegates "unbound", meaning they can vote for whoever they want, but in reality they are being wrangled by the state leafers, and we have the much vaunted brokered election, where it could be anybody. Much horse trading and backroom stuff.
There's also the business of the VP. Since right now Biden hasn't announced his VP choice yet, this also would probably be settled duing the bargaining phase of the brokered convention. I'll throw my states votes your way for a VP spot. That kind of thing. This stays true even if Bid n had announced a pick. The VP has to be voted on and nominated by the convention just lik the president, so an announced pick pre convention probably wouldn't hold up. Too many deals to be made.
Scenario no. 2:
Biden made it to the convention, got nominated, a VP pick was made, and then he died.
This one really sucks for the VP.
At this point the ballot in November is going to say Joe Biden for president no matter what, but the VP is going to have to do all the campaigning by themselves. Let's say somehow the Democrats win the general election. It goes to the electoral college as usual. The vote happens as usual. Now it all depends on if the DNC has their shit together or not. If they do have I together, they've made it clear to the Biden electors to all vote for the same person. If they do, good whoever gets the most votes is the president elect. If they don't, and you have enough random votes that go every where then whoever got the most votes is president elect...which would be Trump. Then repeat the process for VP as usual.
This sucks for the VP pick because there is no guarantee for them that the DNC would give the order to elect the VP vote to the president vote. There's not even a guarantee that they'd keep the VP pick as VP. There's also there is also a possibility that if they don't keep it together that you end up with Pence remaining VP to a democratic president. They don't open the ballot box there you see, and there's no do overs. The box stays locked until a joint session of Congress unlocks it and counts the votes. All that matters is who gets the most votes in the box for each office.
Scenario 3:
Biden lives long enough to win the general election, but dies before the Electoral college meets:
Same as scenario 2, but the VP is probably in a better position to "move up a spot" due to the optics involved
Scenario 4:
Joe Biden somehow dies in the half hour between when the electoral college votes and Congress unlocks the box:
This is the only spot where a constitutional crisis would occur. My best guess would be that Congress pretends like they didn't hear anything and we proceed to scenario 5. Otherwise the supreme Court is going to have to sort this one out. Since Biden won the EC, but Trump is the highest vote getting living candidate, but the Dem VP is VP elect. Either way Pence is out of a job.
Scenario 5:
Biden dies between the Congressional vote count and the inauguration:
This one is simple. At this point the VP has the magic word "elect", and this makes all the difference. The VP elect would become president elect, and we proceed as normal, with the VP spot vacant until the new president submits a name to the Senate for approval. The VP is vacant until the Senate says yes.
Note: in this case Biden isn't posthumously inaugurated or anything like that. No asterisks or the like the VP elect goes straight to the White House.
Also in every scenario expect like a bazillion court challenges, but this is the way it should pan out, barring a retarded Hawaiian judge getting involved or something like that.
