First, this has never really happened in the United States. In extreme emergencies and national disasters, elections have been held a few days late, but never suspended (unlike, for example, the United Kingdom, that suspended elections during World War II). Elections were also not canceled during the Civil War, or as a result of the War of 1812 (during which the U.S. capitol was burned to the ground by foreign military forces).
For example, elections were not prevented from being conducted by the Spanish flu of 1918 which was in all respects deadlier and more contagious than the coronavirus, despite the fact that the technology available for a response in 1918 was less advanced.
Realistically, you would need a disease that is catastrophic on the scale of the Black Plague in medieval Europe (that killed a third to a half of the population in many places), and not merely something like the coronavirus (with a 2% mortality rate), to take out the electoral process in the U.S.
A situation like that would involve the collapse of the entire regime and government, and would send us into uncharted waters.
Second, election laws can be changed quite quickly in an emergency. One could, for example, shift as Colorado has, to a system of near complete all mail in ballots, to reduce the amount of in person interactions that were needed.
The U.S. Constitution does not provide the option of not conducting an election. In the absence of an election, elected offices become vacant and the succession provisions of the law which usually kick in when there is a death during someone's term of office would kick in. U.S. Senate vacancies can be filled in most states by Governors on a temporary basis. U.S. House seats that go vacant must be filled in vacancy elections. There is a line of succession to the Presidency defined by law involving a few key Congressional leaders and the cabinet.