The Hunger Games
The nation of Panem was seperated into 13 states also known as districts. In Panem there are mostly factory workers or you can work in the Mines.
When the end of the world happend the only land mass that was left was Panem, the cause of the disaster was that the sea level was rising.
Some time after the end of the world as we knew it, a nation was established in North America that would soon come to be known as Panem.
You have given a reasonable answer to what might have happened to the USA before Panem was established as a new country in North America - good!
SvarSlett