Likely anything that goes beyond missing out on compensation (ex: unvested RSUs) or even clawing back some comp would violate labor laws. CEOs are still employees, and legislation regulating employer-employee relations trumps all contracts.
There are many many instances where the CEO is not an employee, but they operate via their own legal entity. To be honest I don't know how this works at larger companies.
I'd never heard of this. It turns out it is very rare for publicly traded companies [1]. In these cases, I would guess it comes down to contract terms. But again, it's not as though the law would compel an individual to continue working at a company. It would just come down to what the contracts say, and, potentially, how the courts interpret those contracts in the event of a lawsuit.
[1] Examples I found: Worksport Ltd., Exicure, Inc., Rainmaker Worldwide Inc., and Acorn Energy, Inc.
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[1] Examples I found: Worksport Ltd., Exicure, Inc., Rainmaker Worldwide Inc., and Acorn Energy, Inc.