Hi! I believe you are correct, and we have not received a similar ask before, but I appreciate you checking! I would think it very unlikely that during a time of severe economic depression, states would secede from the US.
No state (not even you, Texas!) is self-sufficient enough to succeed. The immediate and hard withdrawal of interstate trade, subsidies, and federal funding would severely damage the economy even more than the depression. The already sky-high unemployment rates would become even worse as all the individuals with federal jobs lose their positions.
There will be people who think that they would be better off as an independent republic. They may or may not even be the majority. Regardless, they would not be able to secede because the US isn’t going to let go of a state very easily. If citizens try to rebel against the state using violence, they would be no match for the US military. No state’s National Guard would be a match for the US military.
Civil disobedience will probably be present to a degree – probably in the form of protests and riots. If the law enforcement of the state is in full support of secession and the protests, they may not do anything to prevent them. Should rioting get bad enough, the US may decide to take more dramatic actions to provide law enforcement and disband rioting. This would bring us back to the point made in the previous paragraph - no state alone would be a match for US forces.
All that said, this doesn’t mean you can’t have a state secede in your book! It would be interesting to see characters have to deal with the economic and potential military repercussions of a secession –especially if your state is one of the larger ones where there would be a noticeable loss of revenue for the US if the state seceded. Maybe the general public supported secession because of the economic downturn, but what solidified the break-up was that the state legislature was corrupted by another country who promised assistance. The other country may have been interested in this state because it produces a particular product or service that is extraordinarily valuable to that other country.
I hope this was helpful and not discouraging! Best of luck with your novel!