When Donald Trump took the oath of office once again, it was the last time he’d be able to do so under the country’s constitution. But that hasn’t stopped his team from flirting with the idea of running again, writes Alex Hannaford – and the Democrats are nowhere to be seen...
The Constitution leaves what happens if the Presidency and VP are both vacant at the same time up to Congress, and Congress has passed various Presidential Succession Acts, the most recent being 1947. The language in that Act specifically exempts anyone who would otherwise be ineligible from becoming President.
https://en.m.wikipedia.org/wiki/Presidential_Succession_Act
And this has been enforced in the past; Cabinet Secretaries who were not natural-born citizens have not been included in the succession list. I remember specifically that when Madeline Albright was Clinton’s Secretary of State, she was not on the list because she was born in Prague.