If the incumbent loses the election, they usually stay until January of the following year until the elected candidate takes office. If the losing candidate is not the incumbent, the losing candidate, just, goes, home!
No candidate loses until the ballots are counted. How can you be certain that a candidate is a "losing candidate" before the election is held?
De Witt Clinton in the 1812 re election.
Charles Pinckney in the 1808 Presidential election
Rufus King in the 1816 Presidential election
Aaron Burr in 1800 Presidential election
Thomas Jefferson in 1796 Presidential election
Thomas Dewey of New York was the losing Republican candidate in 1948.
candidate by king
Thomas Dewey of New York was the losing Republican candidate in 1948 against Truman.
Candidate - Gov Nova Net
The losing candidate gives a concession speech.
What candidate and party did Fillmore support in the 1864 election