Oh, one more item:

So what that the person no longer works there? An HSA is their own account, not the employer's. You might have a HSA with $$$ in it, and you leave that employer or go on Medicare. You keep that account and keep spending from it. You just cannot keep putting into it, once you are on Medicare. But if you are not, and your new employer has qualifying coverage that you accept, you can start depositing to your existing HSA, again.

Hope that helps.

Maybe they really have FSA.