A university will keep your papers for a set duration as per its policy. For instance, if they are assignment or examination papers, the institution may keep them for a certain period to give a window for solving a grade dispute. Once that window expires, the university can now destroy them confidentially.
In the same vein, an institution can retain an essay paper over a given period. Several institutions opt to retain the soft copies while discarding the hard copies over a specific period in confidence.