If you become unemployed, you are allowed to pay for medical insurance through your old company for 18 months (this is called COBRA). You have to pay the full price that the company pays, and the company is allowed to charge you a fee up to 2% to cover their administrative costs. COBRA does not cost the company, nor the taxpayers, since you pay for the medical insurance.
Some people are unable to find a job WITH BENEFITS within 18 months. Buying an individual policy is unaffordable for most people and families. This petition asks the White House to extend COBRA beyond the current 18 months, until the individual can get comparable health insurance under another plan, for a comparable price.