There is more to this story. No insurance company will send an account to a collection agency unless there is a really strange set of circumstances, like they paid for a false claim, overpaid a claim, uncovered some egregious false application data, got paid by a bad check or had a payment by credit card reversed, resulting in them providing insurance without proper payment.
Another possibility is the insurance premium was underwritten for a certain term and you either did not make the monthly installment payments or cancelled the policy before the term expired resulting in them re-calculating the premium based on the term used. This would be no different than getting the monthly rate at an RV park and then leaving after 6 days. You would be charged the higher, daily rate and if the park had made some kind of payment arrangement and you hadn't paid enough that month to cover the 6 daily rate fees you might owe them money.
When you don't renew an insurance policy after the term has expired, your insurance is cancelled, plain and simple and that would be the end of it. So what is the rest of the story?