You might be able to continue your current insurance, at least for awhile, as part of your divorce settlement. Otherwise, states have insurance policies for those who cannot get coverage elsewhere and/or, there's Government Medicaid, etc.

I have Blue Cross/Blue Shield from my State because private plans will not cover me (I'm obese), it is more expensive but is fine/regular insurance. They have similar but less expensive options for those who are not able to afford more expensive ones. I think California's BC/BS plan is called "Anthem": http://www.anthem.com/health-insurance/home/overview