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I don't know what a "learning hospital" is. Do you mean a teaching hospital? That is the label given to hospitals that host training programs for medical schools - doesn't really have any direct relevance for nursing. Nursing education rotations happen at all sorts of hospitals/facilities.
Any employer can hire a student nurse if she/he qualifies for a job at that organization. Some employers have jobs designed just for nursing students, but you could also work as a nurse aid, transporter, clerk, etc... anything that does not require a license.