When does my employer coverage actually end? - any advice?

HR said my health plan continues for a bit and I do not understand how. I have read a lot of threads here and could not find my exact situation. 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.