The convention is over and the candidates selected. At this point, I have no idea what might happen should this wild-eyed rumor end up being true.
I remember researching this topic on a couple of earlier threads this year.
The short version,
If Biden is incapacitated or withdraws as a candidate before the election, the "super delegates" of the Democratic National Committee will elect a new presidential candidate amongst themselves. There will -not- be another national primary.
More,
Filling a Vacancy: From the Nomination to the Electoral College Vote
Since the time of Andrew Jackson's run for the presidency in 1828, individual political parties have had the job of filling any vacancy on their national ticket, either that of their presidential or vice-presidential candidate.
If one of their candidates vacates the ticket after they are nominated, either because of death or withdrawal, the party selects a replacement.
Both the Republican and the Democratic parties have rules in their bylaws governing how to fill the vacancy. The Party Chair calls a meeting of the National Committee, and the Committee members at the meeting vote to fill the vacancy on the ticket. A candidate must receive a majority of the votes to win the party's nod.
The same process would happen if the vacancy were to occur after the general election but before the Electoral College voting. If a vacancy should occur on the winning ticket, it would then be the party's responsibility to fill it and provide a candidate for whom their electors could vote.
Vacancies of Presidential Candidates
A vacancy could occur at the top of a winning ticket during the period after the electoral votes had been cast but before the President-elect had been sworn in. Perhaps the closest the country has come to confronting this was during the widespread anxiety as the 1861 inauguration of Abraham Lincoln approached, that he would be assassinated before he could take office, or that the counting of the electoral votes (at that time occurring on the morning of the inauguration, which, in those days, occurred on March 5) would be disrupted by Southern pro-slavery sympathizers, neither of which happened.
No President-elect has in fact failed to be sworn in. Nevertheless, the rules for what would happen if a President-elect were to be unavailable to be sworn in actually became a part of our law with the adoption of the 20th Amendment in 1933. This amendment was passed primarily to shorten the length of time between the general election and the beginning of the new administration (inauguration day was moved from March to January). But it also specified that if, at the time of the inauguration, the President-elect has died, then the Vice-President-elect becomes President, and if a President has not yet been qualified by that time, then the Vice-President-elect acts as President until a President has been so qualified. The concern was that, since inauguration day was moved earlier, provision had to be made to cover cases in which the Electoral College vote did not prove decisive and the winner had to be chosen through a possibly lengthy series of votes in Congress.
In the election of 1872, Horace Greeley was the Democratic nominee for President, but the Democrats lost the general election to the Republican ticket, headed by Ulysses Grant. After the popular vote, but before the Electoral College vote, Greeley died. Because the Democrats had no chance of winning the election, given the outcome of the popular vote and the number of electoral votes already secured by Grant, the party did not bother to stipulate to their electors who an official replacement candidate would be, and most of the Democratic electors in the states that the Democrats had won cast their votes for people other than whom their party had nominated.
Vacancies of Vice-Presidential Candidates
In 1912, James Sherman, the Republican candidate for Vice-President (and the incumbent Vice-President under William Howard Taft) died on October 30 of kidney disease, a few days before the general election on November 5. The Republican National Committee scheduled a meeting to be held after the general election, on November 12, to select a successor, and Sherman's name remained on the ticket for the general election. The Republicans lost, however (the Democratic ticket of Woodrow Wilson and Thomas Marshall won), and decided on November 8 not to meet as they had planned because voters only chose eight Republican electors, in Vermont and Utah. These electors did meet later, however, and, acting without instructions from the RNC, voted to replace Sherman's name on the ticket with that of Columbia University President Nicholas Butler of New York. This was a purely formal act with no practical consequences for the election.
During the 1972 presidential campaign, Democrat Thomas Eagleton was Senator George McGovern's vice-presidential running mate for only 18 days. Eagleton dropped out of the race acknowledging that he had been hospitalized three times in the 1960s for depression and stress, and that he had undergone electric shock therapy. McGovern selected the Peace Corps Director, Sargent Shriver, to replace Eagleton, but to actually place Shriver on the ticket, the Democratic National Committee met and chose him in the first week of August. The Democrats lost the general election in November to the Republican candidates, Richard Nixon and Spiro Agnew.
