Earlier quoted context omitted.
You don't "accept someone's resignation" and then add terms to it and actually "resign" them a little sooner than they were going to resign. That's called firing.
That's exactly what a lot of companies do when someone gives 2 weeks notice. Send them home right away and pay them for the 2 weeks so you can keep them from filing unemployment and have them on the hook for any exit interview / handoff questions etc. They always want you to sign "something" as part of the process, too.
You cannot file for unemployment aid if you resign or are terminated for cause. You can only get assistance if your termination is the result of your position being eliminated, otherwise known as a reduction in force. This is valid in California and I believe true in every other state in the US.