Nivolumab in Treating Patients With Persistent, Recurrent, or Metastatic Cervical Cancer

Inclusion Criteria: * Patients must have persistent, recurrent or metastatic squamous cell carcinoma, adenosquamous carcinoma or adenocarcinoma of the cervix with documented disease progression (disease not amendable to curative therapy); NOTE: the following cervical tumors are not eligible: minimal deviation/adenoma malignum, gastric type adenocarcinoma, clear cell carcinoma and mesonephric carcinoma; histologic confirmation of the original primary tumor is required via the pathology report * All patents must have measurable disease as defined by RECIST 1.1; measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded); each lesion must be \>= 10 mm when measured by computed tomography (CT), magnetic resonance imaging (MRI) or caliper measurement by clinical exam; or \>= 20 mm when measured by chest x-ray; lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI * Patients must have at least one "target" lesion" to be used to assess response on this protocol as defined by RECIST 1.1; tumors within a previously irradiated field will be designated as "non-target" lesions unless progression is documented or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy * Appropriate for study entry based on the following diagnostic workup: * History/physical examination within 28 days prior to registration * Imaging of target lesion(s) w…