If these rural areas want to break away and go their own way, they wont have the resources to combat crisis on their own, they can't even do that with their current tax revenue and I don't imagine they are willing to quadruple their property taxes to do so.
I expect they'll whine and yell at other states if they need help. However I'd hope the gov of the remaining area of oregon would flatly tell them no, at least I would.