If you get a new insurance do they pay for previous bills?

Both insurances will work together so that one ends on the day that the other one picks up. The premium rates are prorated, so you may get a refund from the first at some later date. If it is health insurance, for example, the dates of the bills will determine which company pays. You may have to patient for it all to work out, but by keeping an eye on it and being timely with filing your claims, it should all work out.

However, if you are going on COBRA, you have to pay up before they will pay your bills for the period after you ended your job. Good record keeping will help you sort it out.