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 chemotherapy must have been completed \>= 4 weeks prior to enrollment with radiologic evidence of radiological disease progression
• •Eastern Cooperative Oncology Group (ECOG) performance status 0-1
• •Life expectancy of greater than 3 months
• •Leukocytes \>= 3.0 x 10\^9/L
• •Absolute neutrophil count \>= 1.5 x 10\^9/L
• •Platelets \>= 100 x 10\^9/L
• •Total bilirubin within normal institutional limits (except in Gilbert's syndrome)
• •Thyroid stimulating hormone (TSH) =\< upper limit of normal (ULN)
• •Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal
• •Creatinine \< 1.25 ULN OR creatinine clearance \>= 50 mL/min/1.73 m\^2 as calculated by the Cockcroft and Gault formula
• •All radiology studies must be performed =\< 3 weeks prior to the start of therapy
• •Ability to understand and willing to sign a written informed consent document
• •Ongoing prior toxicities related to previous treatments must be recovered to =\< grade 1 at the time of registration (with the exception of alopecia or skin depigmentation)
• •Patients are willing to undergo tumor biopsy pre-treatment (within 14 days prior to registration) and post-treatment (within the first week of cycle 2 onset); patients who consent but have tumor that is not amenable to safe biopsy will be allowed to enter the trial/continue therapy as per protocol if this has been addressed and permission is granted from the lead consortium principal investigator (PI) prior to registration continuation of treatment