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) within 28 days prior to registration * Further protocol-specific assessments: * Recovery from adverse effects of recent surgery, radiotherapy or chemotherapy * Any other prior therapy directed at the malignant tumor including chemotherapy, biologic/targeted agents and immunologic agents must be discontinued at least three weeks prior to registration * Investigation agents must be discontinued for at least 30 days prior to registration * Any prior radiation therapy must be completed at least 4 weeks prior to registration * At least 4 weeks must have elapsed since any major surgery prior to registration * Patients must have had one prior systemic chemotherapeutic regimen for management of persistent, recurrent or metastatic carcinoma of the cervix (e.g.; paclitaxel/cisplatin, paclitaxel/cisplatin/bevacizumab); chemotherapy administered concurrent with primary radiation (e.g.; weekly cisplatin) is not counted as a systemic chemotherapy regimen; adjuvant chemotherapy given following the completion of radiation therapy (or concurrent chemotherapy and radiation therapy) is not counted as a systemic chemotherapy regimen (e.g.; paclitaxel and carboplatin for up to 4 cycles); NOTE: patients who have received more than one prior regimen are NOT eligible * Performance status of 0 or 1 * Absolute neutrophil count (ANC) \>= 1,500/ul * Platelets \>= 100,000/ul * Creatinine =\< 1.5 x institutional upper limit of normal (ULN) or creatinine clearance (CrCl) \>= 40 mL/min using Cockcroft-Gault formula * Bilirubin =\< 1.5 x ULN * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x ULN * Normal thyroid function testing (thyroid stimulating hormone \[TSH\]) within 14 days prior to registration * The patient or a legally authorized representative must provide study-specific informed consent authorization permitting release of personal health information prior to study entry Exclusion Criteria: * Patients who have had prior therapy with nivolumab or with an anti-PD-1, anti-PD-ligand (L)1, anti-PD-L2, anti-cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or immune check point pathways * History of severe hypersensitivity reaction to any monoclonal antibody * Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free for a minimum of 3 years * Patients with uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure and unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patients who are pregnant or nursing; women of child-bearing potential (WOCBP) must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; WOCBP should use an adequate method to avoid pregnancy for 23 weeks after the last dose of investigational drug; WOCBP must have a negative serum or urine pregnancy test (minimum sensitivity 25 IV/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 24 hours prior to the start of nivolumab; women must not be breastfeeding * Women who are not of childbearing potential (i.e., who are postmenopausal or surgically sterile or have undergone definitive radiation) do not require contraception * Women of childbearing potential (WOCBP) is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy of bilateral oophorectomy) or who is not postmenopausal; menopause is defined clinically as 12 month amenorrhea in a woman over 45 in the absence of other biological or physiological causes; in addition, women under the age of 55 must have a documented serum follicle stimulating hormone (FSH) level greater than 40 mIU/mL * WOCBP receiving nivolumab will be instructed to adhere to contraception for a period of 23 weeks after the last dose of investigational product * Should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform the treating physician immediately * Patients with known brain metastases or leptomeningeal metastases are excluded unless the following conditions are met: * Metastases have been treated and there is no magnetic resonance imaging (MRI) evidence of progression for at least 4 weeks after treatment is complete (must be confirmed within 28 days prior to the first dose of nivolumab administration) * There must also be no requirement for immunosuppressive doses of systemic corticosteroids (\> 10 mg/day prednisone equivalents) for at least 2 weeks prior to study drug administration * Patients should be excluded if they have known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) * Patients should be excluded if they have a positive test for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection * Patients with active autoimmune disease or history of autoimmune disease that might recur, which may affect vital organ function or require immune suppressive treatment including systemic corticosteroids, should be excluded; these include but are not limited to patients with a history of immune related neurologic disease, multiple sclerosis, autoimmune (demyelinating) neuropathy, Guillain-Barre syndrome, myasthenia gravis; systemic autoimmune disease such as systemic lupus erythematosus (SLE), connective tissue diseases, scleroderma, inflammatory bowel disease (IRB), Crohn's, ulcerative colitis, hepatitis; and patients with a history of toxic epidermal necrolysis (TEN), Stevens-Johnson syndrome, or phospholipid syndrome should be excluded; patient with vitiligo, endocrine deficiencies including thyroiditis managed with replacement hormones including physiologic corticosteroids are eligible; patients with rheumatoid arthritis and other arthropathies, Sjogren's syndrome and psoriasis controlled with topical medication and patients with positive serology, such as antinuclear antibodies (ANA), anti-thyroid antibodies should be evaluated for the presence of target organ involvement and potential need for systemic treatment but should otherwise be eligible * NOTE: patients are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger (precipitating event) * Patients should be excluded if they have a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration; inhaled or topical steroids and adrenal replacement doses =\< 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease; patients are permitted to use topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with minimal systemic absorption); physiologic replacement doses of systemic corticosteroids are permitted, even if =\< 10 mg/day prednisone equivalents; a brief course of corticosteroids for prophylaxis (e.g., contrast dye allergy) or for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity reaction caused by contact allergen) is permitted * Patients who have had evidence of active or acute diverticulitis, intra-abdominal abscess, abdominal/pelvic fistula, gastrointestinal perforation, gastrointestinal (GI) obstruction and/or who require parenteral hydration and/or nutrition