We have a new TV series here,
Designated Survivor staring
Kiefer Sutherland, based on exactly this scenario. The President is giving the annual State of the Union Address to a joint session of congress, with the SCOTUS, JCOS, and everyone else who is anyone in attendance. And it's a real thing that does happen like that here every year in January. There is always one low level cabinet member, the "designated survivor" kept in a secure "undisclosed location" in case the capitol building becomes a smoking hole.
In the TV show, the new President's legitimacy is thrown into question when it comes out that the previous President was going to ask for the DS's resignation the following day. But since that never happened, he was the DS and ascended to the Presidency when the Capitol went poof.
I highly recommend it. It's a very good show. And Kiefer Sutherland is excellent in the role.
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