I think my scenario is more interesting:
https://uselectionatlas.org/FORUM/index.php?topic=88095.0In brief, a bomb goes off at the inauguration, killing the newly sworn in president and VP, as well as the Speaker and President Pro Temp. At that point, the Cabinet still officially consists of holdovers from the previous administration, because Cabinet terms don't automatically expire on Jan. 20. And so, the previous president's Secretary of State could arguably be sworn in for a full four year term.
