ezine articles are for marketing purposes and link building purposes. They don't pay authors for articles. The benefit of publishing an article with article databases (e.g. ezine Articles, Article City, etc.) is that the author can include links back to their own websites.
One way that freelancers can make money with ezine articles is to team up with someone (like a business owner or internet marketer) and write articles on their behalf. From what I understand these gigs don't pay much generally, but it's a potential way to earn some cash.
Hope that helps!