Not exactly. If you leave a job with money remaining in your FSA and you're eligible to elect COBRA, you'll have an opportunity to continue to make your regular FSA contributions. But you'll make these contributions with after-tax funds rather than pre-tax funds, and the employer can charge an administrative fee of up to 2%. The advantage is that you'll continue to have access to funds that are in your FSA, rather than forfeiting that money to your employer.