My employer asks this question. I refused to answer when asked in person/phone. As we got further in the hiring process they asked as part of the form they fill in to setup the background check. Again I refused to answer this question. I failed the background check due to this.

When we discussed it they said it was necessary so they could verify if I had lied about my salary when I'd given it previously. I pointed out that I had never given this information. HR insisted that I must have since they require it. Round and round we went for a while.

Eventually they let it go and hired me anyway.

So to answer your question. Companies will typically call up your previous employer and ask if the salary you provided them is correct.

Lying on your application form is almost always cause to fire. So if they ever find out you lied you about your previous salary you can be fired on the spot.