If your previous employer was big enough (>20 employees I think?) they have to offer you health insurance through COBRA. You would pay the full cost instead of the employer subsidized cost, but you have 60 days to sign up and then 45 to pay and it's retroactive, so if you sign up and pay all premiums on time it will be as if you had insurance the whole time. As far as penalties a certain amount of gap is ok, although I'm not sure how much of a gap, but I'm pretty sure you should be fine.