One company I worked at had a non-compete but never enforced it when occasionally an employee would jump ship to a large client. I don't know if there was any sort of back channel communication or gentleman's agreements in place when this happened to not enforce it. However, I think there would have been more hires by clients if it didn't exist.
My wife's company did sue a former employee who went to a direct competitor. That's the only time I've actually heard of a non-compete being enforced within my own network, so it happens, but it seems rare.
If the employee was laid off, I doubt the employer would enforce it. I think such employers would be extremely rare, but I'm sure such an ******* is out there.