The 20th Amendment was adopted in 1933 and addresses the possibility of an absent president elect with only a little bit of confusion. Section 3 says, "If, at the time for the beginning of the term of the President, the President elect shall have died, the Vice President elect shall become President. If a President shall not have been chosen before the time fixed for the beginning of his term, or if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified; and the Congress may by law provide for the case wherein neither a President elect nor a Vice President elect shall have qualified, declaring who shall act as President … until a President or Vice President shall have qualified."
As we all anxiously observed last time around, the presidential race isn’t really decided the way other races are. Our votes are nice, but technically they are only cast for "electors" who have committed themselves to vote for one candidate or the other. And technically speaking, those electors are free to disregard what we tell them – something that has in fact happened a time or two in our history. No federal law would punish them for such a deviation and some states, as I remember it, don’t even penalize it at all. Others only have the equivalent of a slap on the wrist.
So, let’s say the votes are in and it looks like President elect Tucker will be taking the oath on January 21 – but then this fine person, the last honest politician of our lifetimes, decides to bag the job and get rich on the lecture tour instead. What happens? Well, if the Electoral College hasn’t met yet, Janel can tell the "Tucker Party" electors what to do and maybe they will listen or maybe they won’t. Most likely, state law will kick in and the electors will be instructed by state legislators about what to do – which they will then be free in at least some cases to disregard if they so choose. Once the Electoral College meets to cast its votes and have them tallied in Congress, assuming there are no controversies about any state’s electoral slate, *then* we will have a president elect.
OK, so what happens if Janel waits until after that declaration before making a sudden career change? The oath of office is "only" a ceremony; it isn’t as if a double could stand in for the President elect and, by virtue of having taken the oath, become the President him/her/"it"self. Once the President elect has been chosen, the power is transferred automatically on the magic day. If the President elect dies before the transfer, normal succession kicks in and the office goes to the VP elect. If the President elect resigns, the same thing happens. If both President elect and VP elect resign, the Speaker of the House gets the job. Sound familiar? As I understand it, once the election has been fully decided, we pretty much have a done deal and regular succession is the order of the day.