Two Short Answers:

COBRA - This is the type of insurance you have a right to purchase in the use when you leave your job. You can purchase coverage up to 36 months. Interestingly, you have up to 30 days to purchase it when you leave your job and the coverage can be retrospective. This means if at day 29 you have an injury, you can purchase coverage on day 30 and it will cover the injury. The coverage isn't cheap though.

Exchange - A more affordable option may be to shop a policy on your state or the federal insurance exchange. Typically these policies are less expense than COBRA but can be more difficult to understand as a consumer as there are usually more options. Enrollment periods may also be limited, so you can shop the policy ahead of time to ensure you can enroll with it during your time off.

In summary, two main commercial options in the US, Cobra and the exchange.

There is also Medicaid which is government sponsored health insurance for the economically disadvantaged, but you need to pass the income test and applying can be burdensome. Check with you state Medicaid agency on details.