Severance and unemployment, do they overlap?

I was offered severance of 4 weeks after being let go as a store manager and I am unsure how it affects benefits. The agreement mentions a release and a payment schedule. How did your state treat it?

Rules differ by state. I called the claims line and asked directly, then wrote down the answer and the date.

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