If you're in Canada, there are two options:
- Some insurance companies will offer employee benefits coverage to companies with as few as 2 employees.
- You can join an association plan (there are many out there), where you're part of a larger pool of many small companies and the claims & premiums are spread across the entire pool.

Depending on the size of the company you are leaving you may be entitled to up to 18 months of continued coverage with a Cobra plan. It is usually quite a bit more than you were previously paying, but it allows you some time to look for insurance.

I don't know much about it, but the new state exchanges created by the Affordable Care Act may be worth checking out if you are going to have a limited income. healthcare.gov.

You can also find some health plans and coverage options online through at sites specially designed for self-employed professionals such as StartupInsurance.com and HealthAviator.com.

Cobra is expensive, your best bet is to utilize the cobra election period for free coverage until you are forced to elect, then get on the Healthcare.gov insurance. If your income while you start the company is below thresholds, you will be eligible for substantial subsidies that will help make the coverage far cheaper. Your location may have a state exchange (CA) or you may have to use the federal exchange. You can also buy individual policies straight from a broker or carrier and those are mid priced options to the other two alternatives.

Are you eligible for COBRA continuation coverage? Most employers are required to offer it for a period of 18-36 month (but most likely you would be responsible for paying 100% of the premium).

For more info, see:

http://www.dol.gov/ebsa/publications/cobraemployer.html
http://www.dol.gov/ebsa/faqs/faq_compliance_cobra.html

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.