Then either the people given the deadline are being "managed out of the business" or they should be managing their own way out

And yes, I've been a manager in a company where the phrase "managed out of the business" was used. I no longer work there.

The term that is usually used in law is "constructive dismissal".

Management would tell you it certainly wasn’t constructive dismissal as that’s illegal! ;)

Yet you still won't get those unemployment checks if you were a new hire.

At one company I worked for, they fired the product manager, then fired all of them.