I have my security settings on Facebook set so that only friends of friends can contact me.
Even then, if I get a friend request from someone I don't know, I'll check out their page: where they live, who we know in common, what work they do, if their photos look creepy. They may have their security setting set as high as mine, in which case I won't see much. That is fine. If I can't see a reason why I would want to be friends with the person, I'll click the Reject button.