In the US, there is only one labor law that is different for execs and high paid employees and that is overtime rules. Fiduciary duty does govern how a director or officer behaves while in the role, loyalty, no self-dealing, no stealing corporate opportunities etc. It doesn't oblige them to stay or dictate how they must leave.

In US and English law, "specific performance", so a court ordering you to do what you promised, isn't available for personal service contracts. In the US that's reinforced by the 13th Amendment's ban on involuntary servitude. So even if a CEO signed a contract promising 6 months notice and a smooth handover, the company can't make them do it, they can only enforce any financial penalties that are contracted.