Well, if a U.S. president refuses to budge from the office after losing an election, that’s basically uncharted territory, but let me give you the gist based on laws and stuff. First up, the U.S. Constitution clearly outlines the process for election, inauguration, and the peaceful transfer of power. The 20th Amendment says the term of the President ends at noon on January 20th after an election. If he or she doesn’t leave willingly, the newly elected president is still sworn in. Practically, from that moment, the military and federal agencies would recognize the authority of the new president. So, if the old one doesn’t move, they physically could be removed by Secret Service or federal marshals. Of course, this never actually happened, so it’s all theoretical, but the laws are pretty clear about the end of a president’s term!