> If an employee, for example, decides to put in notice and then half-ass their job until their departure date, a company could actually sue the employee and win.
That sounds rather exaggerated. There may have been cases of an employee being sued for damages by their a employer for not performing their jobs well, but I've personally never heard of them and without digging deep into courts records, I doubt there are many of these.
The reason I highly doubt that, is that even just firing employees in Japan who are half-assing their job requires going to court and providing ample evidence that the employee has been continuously under-performing even though they were notified, given opportunity and failed to improve.
This standard is considered so high, that Japanese companies rarely fire employees for this type of reason (Ordinary termination 普通解雇 futsuu kaiko). When companies absolutely want to get rid of a certain employee, they often prefer to slowly make the employee's life miserable by giving them them demeaning tasks (or in some cases just no tasks at all!), bullying them and cutting their pay — a practice generally called iyagarase (roughly translated as "making someone feeling unpleasant"). That kind of play can also land the employer in legal trouble, but at least the burden of proof would fall on the employee. In many other cases still, companies just keep around employees that are under performing or convince them to take an voluntary retirement package.
In addition to all of that, employment contracts generally require a 30 day notice before quitting in Japan (I guess this is the maximum set by law). Combine that with the fact that most employees tend to have at least 14 days of unused leave accumulated, which they'd use just before leaving, they're not left with so enough working days in which they can half-ass their jobs.
I'm not quite sure about breaking your contract for contract employees, but it the original example ("I'll be threatened that I will have to pay damages for quitting") doesn't seem like a contract employee, and the term "black companies" and the discourse around usually refers to full-time employment. It's probably just threats, as the quote says. Managers sometimes say the craziest things to scare their companies out of quitting.