Severance and unemployment, do they overlap?

I was offered severance of 4 weeks after being let go as an office manager and I am unsure how it affects benefits. I worked as an office manager before this. The agreement mentions a release and a payment schedule. Who should I ask before signing?

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 6 months ago, and it settled down once I kept a simple log of every call and form.