Indirectly, and I supposed directly they can earn money on FB. They can have a fan page or landing page or home page on FB which advertises a product. It doesn't advertise directly, but it can say (for example, they've written a book, this is what it is abut and 'x' i where it is available.
Or, they can direct traffic to their FB page which then directs parties which may be interested in what they have to sell, to a different sales page.
Recently a person wrote a book about his specialty, and explained part of it on my blog AND on his Facebook page.It was so well written that I''m sure that more than one person was so intrigued by his article that they bought the book.
This is a good reason to have everything you publish here or on a blog be printed on LinkedIn, Facebook, Twitter, and other social media. You never know who is going to read what you write and then be enticed to by a book, some PLR articles from you. So, long story short, you can make money by establishing a Facebook presence, a presence on all the social media sites.
The social media sites are not just for talking about your grandchildren or catching up with old high school chums any more. They can be used professionally, so if you intend them to be used professionally, keep the content to professional or above reproach content. (For many people, that means no political diatribes). But, if what you're promoting is political, it is entirely alright to voice political opinions on your site-but I wouldn't encourage political diatribes that have gone south, or that are full of name calling.