I do not have any case studies, but over my 25 years of teaching fourth grade (9 and 10 year olds), I have kept up with numerous students and their families. I recently attended two weddings of former students, I have been one of the pall bearers at the funeral for one of my students, and met in June with one of my former students (he is now 29) who was in a diving accident and is currently paralyzed from mid-chest down.
I don't try to solve any personal problems my students are involved in, but I am a very good listener and will try to help them sort out their options. As an example, during summer school in June, a former student (now 16 years old) whose younger sister was a student at the summer school, talked to me several times about the hard times he was going through. I listened, showed that I cared, and suggested some resources to help him out (such as his school counselor and constructive organizations he could get involved with).
I agree with you: Learn your students (get to know them) to make them learn.
The approaches to defusing any problem of students seemingly center communication and organization. Open interaction between student and instructor through formal and informal feedback allows for a dynamic classroom environment that is beneficial to most individuals involved. Keeping in touch with your students is crucial, on several levels: you look for nods of understanding or grimaces of despair, and you listen to the students when they voice their concerns after class or in office hours. Showing that you respect the students and their varied points of view is just enough to resolve most conflicts before they occur. In addition to communication, organization and preparation can help to avoid problematic issues before they begin. Focusing on the syllabus and establishing "rules of engagement" at the beginning of the course sets the standards in the classroom. The combination of an open dialogue and a clear organization can provide the basis for a structured yet changeable classroom that can meet the needs of both instructor and student.
Each of us has been this kind of student before, frustrated, silent, manipulative, brilliant, totally secure in our previous knowledge… It's just a matter of expanding our perspectives to include all of these mindsets, remembering what we used to be, how we overcame our innocence and our flaws, and helping our students reach the same place.