Health insurance is one of the biggest concerns for employees who lose their jobs -- not to mention their spouses and children. So many of us get our health care coverage through work, and often at a much reduced cost. Federal law gives employees the right to continue their group health insurance coverage after they quit, are laid off, are fired (for reasons other than gross misconduct), or have their hours cut to below the employer's threshold for eligibility. Spouses and family members can also continue coverage for these reasons, or if they lose coverage through the employee in other ways (for example, through divorce or death).
There's a big, big catch to COBRA coverage: You have to pay the full premium, including whatever your employer used to pick up for you. But at least you'll be paying at the employer-negotiated group rate, often much lower than what you'd have to pay for an individual policy.