"Elected officials in the U.S. have also refused to step down, albeit from lower offices than the presidency. In 1874, a Texas governor locked himself in the basement of the state capitol building after losing his reelection bid.
The saga began when Republican Governor Edmund J. Davis lost the 1873 election by a resounding 2-to-1 ratio to his Democratic challenger, Richard Coke, and claimed that the election had been tainted with fraud and intimidation. A court case made its way to the state's supreme court.
All three justices, each of whom had been appointed by the incumbent Davis, ruled that the election was unconstitutional and invalid.
Democrats called upon the public to disregard the court's decision, and proceeded with plans for Coke's inauguration.
On January 15, 1874, Coke arrived at the state capitol with a sheriff's posse, and was sworn in to office while Davis barricaded himself downstairs with state troopers. The next day, Davis requested federal troops from President Ulysses S. Grant. Grant refused, and Davis finally stepped down three days later."
"If Trump were inclined to overstay his term, the levers of power work in favor of removal.
Because the president immediately and automatically loses his constitutional authority upon expiration of his term or after removal through impeachment, he would lack the power to direct the U.S. Secret Service or other federal agents to protect him.
He would likewise lose his power, as the commander in chief of the armed forces, to order a military response to defend him. In fact, the newly minted president would possess those presidential powers.
If necessary, the successor could direct federal agents to forcibly remove Trump from the White House. Now a private citizen, Trump would no longer be immune from criminal prosecution, and could be arrested and charged with trespassing in the White House.
While even former presidents enjoy Secret Service protection, agents presumably would not follow an illegal order to protect one from removal from office."