I’ve wondered about this in the past, but it has really come to the fore in this election cycle. Given that the American electoral system runs on a strict timetable with an election on a date certain, there seems to be scant provision for dealing with the disappearance, death, resignation or otherwise last-minute removal of a major candidate. It has happened in the past, I think in non-Presidential elections (wasn’t the last major case the election of a Senator from Missouri who then died before he could be sworn in?). But we have no Constitutional way to either delay the election to enable selection of a replacement candidate, nor the necessary time built in to introduce that candidate to the electorate.
I would not be at all surprised to see a Constitutional Amendment proposed to handle this very issue within the next few years. For now, it seems that the election would have to move forward as planned, because for the President to cancel a presidential election by executive order would smack too much of tyranny, and there seems to be insufficient time for Congress to pass anything more than a stopgap bill for the President to sign in time for it to occur. (And that’s even assuming the Congress as currently constituted would be amenable to a delay in the first place.)