I know someone who has already served two1 terms as president cannot be elected president again, and there is apparently an argument about whether or not such a person can be elected to vice president.
But presumably a former president can go and become Representative of their district.2 And as a Representative, they could conceivably become Speaker of the House. That puts them third in the line of presidential succession. Various positions further down the line are similarly conceivable.
As such, it seems possible that a former president, not eligible to be elected to another term, could find themselves in a position that would otherwise succeed to the presidency. Is there any caveat in the line of succession that “skips” a former president in such a case?
Or one-and-a-half terms, in cases of someone succeeding a president and then getting re-elected.
John Quincy Adams did, for example, though admittedly he only had one term and that was well before the twenty-second amendment anyway.