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.
Yes, CEOs pay taxes on income. The only way around that is to structure the compensation so it's not income, and the IRS probably has tried to prevent that as much as possible. I'm not a tax or HR expert but I'd think unrealized gains on stock compensation might not be. Deferred compensation might not be, until it's actually paid.
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.