Claims submitted after insurance plan ends

Hi, my daughter had surgery before I changed jobs. Hence insurance would be changing but the new job has a 30 day period before I can sign up for a new plan. She had it on Nov 13th and my plan didn’t end until Nov. 27th. I had a baby, my son had surgery and my daughter, we had all met our individual 700 dollar deductibles minus 400 for my daughter which we paid to the hospital before her surgery. Some how we are getting bills showing insurance paid 0.00 for the anesthesia when my son had surgery earlier this year at the same hospital and it was 100.00 after insurance paid. I can see it says the claim was submitted Dec 2. Would they have run it and then saw I had no insurance at that date and that be it even though date of the surgery was done on 11/12 ?!? I’m trying to figure out what questions to ask when I call bc the office of the doctor who performed it never seems to understand anything either. I pay a 45 dollar copay every time I go and still get a bill in the mail for the same 45 dollar copay that says I haven’t paid it and I’m constantly having to go through that with them. What questions do I need to ask. I wish I could post a pic of the EOB