Exception 2: Digitizing Unpublished Work For Preservation Or Research
§ 108. Limitations on exclusive rights: Reproduction by libraries and archives
(b) The rights of reproduction and distribution under this section apply to three copies or phonorecords of an unpublished work duplicated solely for purposes of preservation and security or for deposit for research use in another library or archives of the type described by clause (2) of subsection (a), if —
(1) the copy or phonorecord reproduced is currently in the collections of the library or archives; and
(2) any such copy or phonorecord that is reproduced in digital format is not otherwise distributed in that format and is not made available to the public in that format outside the premises of the library or archives. (US Copyright Office, n. d.)
Librarians may digitize an unpublished work for preservation or research if the library owns it and it isn´t available digitally. However, the library may only use it on-site and cannot put it on its website or loan it to other libraries. This exception might be relevant in the case of dissertations or other student work.