Severance and unemployment, do they overlap?

I was offered severance of 16 weeks after being let go as a call-centre agent and I am unsure how it affects benefits. I also wonder about the job-search requirement. How did your state treat it?

Keep everything in writing and save the confirmation numbers. It saved me later.

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.