Can an employer find out if you’ve been fired?

I’m curious if a future employer can find out if you’ve been fired from a previous job, and if so can they find out the exact reason for that?

I’m guessing via background checks they can find out where you’ve worked, even if you don’t disclose a specific employer because you’ve been fired from them.

If they do call the previous employer, can they find out the exact reason why you’ve been fired? I can’t seem to get a straight answer on this.

Thanks.