Ipilimumab in Treating Patients With Metastatic or Recurrent Human Papilloma Virus-Related Cervical Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed metastatic or recurrent cervical cancer of squamous, adenocarcinoma or mixed histology type not suited to definitive localized therapy; HPV status will be confirmed for all patients following enrollment * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \> 10 mm with computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam * Previous therapy: * Patients may have undergone surgery and/or received definitive radiation or chemo-radiation for localized disease in the past * Radiation treatment with curative intent (radical chemoradiotherapy or adjuvant chemoradiotherapy) must have been completed \>= 3 months prior to enrollment * Note: patients who completed palliative radiation therapy 2 weeks before start of ipilimumab are allowed as long as this does not affect measurable disease * Patients must have been exposed to platinum chemotherapy either as part of definitive chemo-radiation OR as first line systemic treatment for metastatic disease * Patients MAY have received up to two prior lines of systemic chemotherapy for metastatic or recurrent disease; patients with metastatic disease at first presentation MUST have received one platinum based line of chemotherapy * All chemot…