It is not uncommon for paperwork to be delayed when switching insurers. I've had it happen at previous employers. The normal course of action in this circumstance is that you pay the bill after your insurance paperwork is sorted out.
If you go to the hospital and didn't know that your insurance expired, you probably won't even see a bill for a month, after the hospital gets the denied claim from your previous insurer. At which point, you'll give them the updated information, and they'll file the claim with the new insurer.
If you go to the hospital and didn't know that your insurance expired, you probably won't even see a bill for a month, after the hospital gets the denied claim from your previous insurer. At which point, you'll give them the updated information, and they'll file the claim with the new insurer.