When does my employer coverage actually end? after 4 years as an event coordinator

I was told my coverage ends on my last day, but the letter says the end of the month. I worked as an event coordinator before this. I have an appointment next week. What should I do about appointments?

Keep a copy of any coverage confirmation in case of later disputes.

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