Can a business send a bill to collections even if you've been paying on it every month?

I’m so mad I can’t see straight. We had three bills at the hospital that I’ve been paying on every month. I paid one of them off completely about six months ago. I have $40 left on one more, and $380 on another.
I get statements from them every month which I pretty much ignore because I know what I owe.
Well, today I got a suspicious looking letter from “someone,” and it turned out to be a collection notice from a collection company for the $380 I owe on the one bill!!!! I went through the roof! Then I opened up one of the statements from the hospital. IT was a nasty letter dated Oct 31st, saying that I’d been ignoring repeated attempts to contact me! That statement said I owed $400. Why did the collection statement say I owed $380 rather than $400? Because I had made a $20 payment at the beginning of November before I ever even got that notice!
I have made payments every single month. Can they still send it to collections? And when I made the payment in November, in person, at the billing department at the hospital, why didn’t the gal who processed the payment tell me that it was getting ready to go to collections???? And why didn’t someone call me???
I’m so mad.