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If a person cannot hold an office, they are typically also disqualified from running for said office, for exactly that reason. What would you do if an ineligible person won the election? That would be utter chaos.
Someone explained to me there is a procedure for an elected candidate who is ineligible actually wins the election.
If for any reason the president cannot carry out the duties of the office, it falls to the vice president. So you’d have to just skip the president and swear in his running mate.
It would still be utterly stupid, but surprisingly there is a process to handle the scenario.