If you receive a severance package from your employer (i.e., 12 months' severance pay), can you still apply for unemployment benefits?
It depends on the state. In Illinois, you can receive severance and unemployment compensation both without it affecting your benefit.
In VA I was always told to apply and they will determine your eligibility. They can make distinctions for vacation payouts, notice period payouts, circumstances of separation, severance, etc. I usually got retroactive payments to my date of separation regardless of my deal with the employer. It is an insurance plan paid for by you, through your employer, and I would take full advantage of it.
We were told that we couldn't apply for unemployment while receiving severance which was paid out monthly, but we did apply and received unemployment. This is in New Jersey.