They'd usually have to prove they fired you with cause not because you said you quit.
i.e. if you get caught stealing or are sexually harassing your co-workers, they can still fire you. They are not however required to let you work. They can revoke access and continue to pay, they can give you a package and terminate you employment. If you don't want to take the package, they can just walk you out of the building and terminate your employment two weeks later.