Employment and salary verification reference checks are common, I still receive them for ex employees of a small company started and sold years ago. It happened at my last few jobs in tech. BTW, they don’t have to ask you for any, all they have to do is call the company listed on your resume.

There are also informal “reference checks” though, where people who know each other talk about you, and even these are just one of many ways that your reputation can follow you. Leaving behind something very noteworthy like telling your bosses off and taking other employees with you is a good way to have people sharing stories about you.

I hadn't had any references checked, much less even requested in probably a decade... that is, until my current job. So some do still do it, but apparently not many.