Am going to disagree with you on this topic. Facebook does not own or run fake accounts for selfish reasons. Am certain on this because I've done an extensive research on it. Asides that, facebook is close watched and regulated by relevant authorities. I own three facebook pages with over 200k followers acquired through facebook's paid audience reach. I have personally checked to make certain they are real people on those accounts.
Just like every other online medium which connects businesses to individuals or vice versa, facebook runs a unique marketing model which is solely focused on reaching target audiences. It's a process that allows paid ads get to people who have shown interest on the said ads topics thereby yielding results on reachs and clicks, or even followers.
If you pay close attention to facebook pop-ups, then it's likely you've come across certain page suggestions based on your profile's interest, interests which you picked when registering on facebook or based on your recent activities. This is how facebook generates likes and followers for clients through paid ads. With over 2 billion users worldwide, facebook has no problem getting your target audiences.
Hence, those accounts that seem fake and show up from nowhere following pages and liking post do so because the services has been paid for, for facebook to solicit on the page's behalf to a much larger audience which on normal grounds would be impossible for the page to reach on it's own.
Remember that individual accounts are free and equally free of facebook business methods. It's only normal that a facebook page runinngs will look very much different to a user unfamiliar with it's operations. A facebook page on the other hand is a marketing channel designed for business models, and as such services has to be paid for in order to maximize it's full potentials. This is the reason why page administrators get regular paid ads suggestions for gaining certain number of reach depending on the request.
Note: the whole process explained above is one of the major means which facebook utilizes to make money.