"Liberation Day" at OpenAI as multiple senior executives announce leaving

Yes, it's extremely uncommon for a company to say they had to let an executive go. Not least because it reflects poorly on the judgement of the people who hired them.

"We wish them best of luck in their future endeavours", or something similar, is usually what you get out of the company.

Larger corps may even shy away from providing details of malfeasance to future employers reaching out for info on the employee, fearing a lawsuit, so will confirm the person worked there during the timespan they say they did, and that's about it.

Yes, regardless of why you left.

If you did something wrong, obviously you won't be announcing that and admitting to it.

If you did nothing wrong but were forced out, you will likely still keep quiet because complaining loudly about your employer is really bad for your prospects looking for future employment. You may also earn yourself a lawsuit for defamation or breach of contract.

Despite the obvious loss to the world in keeping that truth hidden, it's generally in your best interest to keep your head down and move on, lest you become the target of a billion dollar corporation.

To lie about it, Sure. Not sure if they realize that in some cases it's very transparent

I wouldn't know for sure and I'm clearly guessing.

But if you look at the units who's executives are leaving (Sora and such) and then put two and two together - a different plausible picture emerges that they might have been asked to leave.

What an executive on Sora is supposed to do when Sora itself is no more?

There's a spectrum of voluntary-ness here. It's one thing if Sam Altman calls you up to say "I will fire you tomorrow if you don't resign today".

Is it a lie if he says "well, hmmm... it's really unfortunate that your project got shut down... I'm not really sure where to put you..."?

What if you still have a job to do, and nobody's said anything about imminent problems, but it's clear you've burned trust that you won't be able to reclaim?

What if the new work available to you is a big step down, and you think if you moved to another company you might not have to take that step down?

Yes, that's professionally expected from senior management (and below). You never wash your dirty laundry outside. Public departure reasons are lies, that's professionally understood by all involved parties and usually all benefit from those white lies.