When does my employer coverage actually end? - what worked for you?

I was told my coverage ends on my last day, but the letter says the end of the month. It has been weighing on me all week. I do not want to be surprised by a bill. Did coverage match what HR said?

Thanks for writing this out. I went through something close to it 14 months ago, and it settled down once I kept a simple log of every call and form.