When a vehicle is sold, insurance typically doesn't transfer to the new owner. What usually happens is the title will be put in someone else's name and that person will receive a notice to see if they wish to renew the insurance. Although in this case it was stated that the title is still in the original sellers name so the insurance company may not even know that the vehicle is in possession of someone else, but I don't think someone who sold a car will willingly continue to pay for it's insurance every month. So we're left with a couple of ways to verify what's going on.
A good way to find out is to just contact the DMV. They will be able to tell you the status of a vehicles registration, insurance and any outstanding fines or tickets there may be. The information required for this should simply be the make, model, license plate number and VIN number. The VIN is a 17 character long code that can be found by looking at the dashboard from outside the vehicle and is typically located on one of the bottom most corners. Read more about how to decode a VIN number.
Another method to check if a vehicle is insured is to simply call another insurance company and ask them to verify for you if your car is insured. You can mention that you want insurance but actually do not remember if you are currently insured or not, they cannot sell you an insurance policy when there is already an existing one.
I know how frustrating and exhausting issues of this nature tend to be but good luck with it and do not stop asking questions until you have what you need!