If a person just generally thinks a company is poorly run and decides to quit, would shorting the stock count as trading on non-public material information? If it's not based on any specific piece of information, could one not plausibly say both one's departure and the shorting was out of spite for the company? Alternatively, if a person is a minor figure in the organization but is fairly essential to the future growth of the company, if that person quits and then buys put options, would that fall foul of insider trading laws?
The law is somewhat nebulous but from what you are describing I would say "no".
As anyone can post and read reviews on glass door or something similar, it could be common knowledge of the management woes. Heck it might even be in the company's press releases but one would have to read between the lines. (Example the CEO's brother is the CFO and his cousin the the CTO and their resumes or education do not support those roles).
As far as the person who was essential to the company's growth...was their hire announced via press release? If not then neither would their departure and so as such it is immaterial.
Leaving and then deciding that it is so poorly run that they can't help but lose money would not qualify.
Illegal insider trading is when someone uses material nonpublic information (MNPI) to gain an advantage. Thinking that a company is run poorly isn't MNPI, it's just an opinion. However, knowing that the entire management team that brought success to the company is going to be replaced by the co-founder's son and his drinking buddies for no reason except nepotism would definitely be nonpublic information, and almost certainly material as well.
There's no hard-and-fast rule of what constitutes MNPI. The nonpublic part is easy - anything that isn't made known to the general/investing public. But materiality is on a sliding scale. The above example is so extreme I can't imagine it not being material. But a CEO stepping down to be replaced by another qualified CEO may not rise to the level of being material (if you know that information ahead of time, it would still be risky to trade on it in case the SEC does determine you traded on MNPI).
If a person is a minor figure in the organization but is fairly essential to the future growth of the company, if that person quits and then buys put options, would that fall foul of insider trading laws?
Possibly, but probably not. If they're a minor figure in the organization, then their impact on the future growth of the company is probably small. If they're the sole inventor or idea generator, or do something that nobody else can do (i.e. they're irreplaceable), then they're definitely not a minor figure.
To protect itself, a company may place a post-termination trading restriction on an employee or executive to prevent them from trading on any MNPI after leaving the company, usually through the next quarterly earnings release. Someone with sales data, financial information, information on R&D progress, etc., might fall under that category. While not being under a restriction like that when you leave isn't a guarantee that you don't have MNPI , it often does mean that the company feels like any information you're leaving with isn't material.
This is in a very gray area, and you should only consult with a lawyer to get a reliable advice. The answers you get here worth exactly what you paid for them, but hear this:
Insider trading is trading based on information not available to general public. If you're that material person and your departure was not announced to the general public but you know how it would affect the company performance - trading on that knowledge is most definitely insider trading.
The fact that you're no longer employed doesn't matter for insider trading rules. The information you were exposed to is still confidential to the general public, so you're still not allowed to trade on it.
The enforcement of insider trading rules is done based on facts and circumstances of specific cases. If SEC can show that your trading pattern was abnormal, you were trading significantly differently than other investors, and that you've benefited where they lost - they will probably have a better case to prove that you did all that because you used some knowledge you gained while being employed. They might even not need to point to the specific knowledge, just the opportunity to have it.
That said, as mentioned in the first sentence: for reliable legal advice (where you can use "advice of counsel" as a criminal defense) - talk to a lawyer.