http://www.columbia.edu/cu/isso/visa/F-1/F-1_reinstatement.html
Option 2 is incorrectly understood by you
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You probably understood it wrong. Usually option 2 is called reinstatement of status, the student doesn't leave US, and it is an administrative application, not a lawsuit.
http://www.columbia.edu/cu/isso/visa/F-1/F-1_reinstatement.html
http://www.columbia.edu/cu/isso/visa/F-1/F-1_reinstatement.html