Most employers won't confirm the reason for termination with random callers who are verifying employment history.
Unemployment insurance is a bit different. When a former employee files for unemployment benefits then the state will notify the last employer, and that employer can dispute the claim if the termination was for cause. In practice many employers don't dispute unemployment claims even for employees whom they terminated for performance reasons because it's not worth the hassle.
The rate that employers pay for unemployment insurance is tied to the number of claims. While they wouldn't dispute in bulk for layoffs, it is worth the hassle when it's for cause.