Severance and unemployment, do they overlap? after 13 years as an accounts payable clerk

My employer is paying severance in instalments and I am not sure whether to file now. The agreement mentions a release and a payment schedule.

Before signing, I asked a friend who is a lawyer to look at the agreement. It was a short conversation and worth it.

I filed on day one anyway and reported the severance honestly. The agency decided what to do about the timing.