Nivolumab and Yttrium Y 90 Glass Microspheres in Treating Patients With Advanced Liver Cancer

Inclusion Criteria: * Patients must have a diagnosis of hepatocellular carcinoma (HCC) confirmed by American Association for Study of Liver Diseases (AASLD) guidelines with a Childs-Pugh score of A or B (but, =\< Childs score B8) * NOTE: If the patient does not have histological confirmation of disease by biopsy, diagnosis of HCC must be documented with approval by a tumor board or other multidisciplinary conference * Patients must have at least 1 lesion that is measurable using RECIST guidelines. NOTE: A previously irradiated lesion can be considered a target lesion if the lesion is well defined, measurable per RECIST, and has clearly progressed. NOTE: For patients with infiltrative disease, evaluable disease needs to be confirmed by pathology if RECIST measurements cannot be made. * Patients must have advanced disease that is not amenable to transplant or resection * Patients may be treatment naive or have received any number of prior therapies * NOTE: Prior immunotherapy is contraindicated and not permitted * Patients with chronic hepatitis B are eligible as long as they have evidence of ongoing viral replication (detectable hepatitis B surface antigen \[HBsAg\], hepatitis B envelope antigen \[HBeAg\], or hepatitis B virus \[HBV\] deoxyribonucleic acid \[DNA\]); they must have HBV DNA viral load \< 100 IU/mL at screening; in addition, they must be on antiviral therapy per regional standard of care guidelines prior to initiation of study therapy; if not on antiviral therapy at screening, then the subject must initiate treatment per regional standard of care guidelines at the time of consent; both HBeAg positive and negative patients will be included * Patients positive for hepatitis C are permitted if controlled with medication, in the opinion of the investigator * Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 * Patients must have adequate organ function within 14 days prior to registration as determined by: * Hematological (without growth factor support) * Hemoglobin \>= 8.5 g/dL (without the use of growth factors) * Absolute neutrophil count (ANC) \>= 1000 * Platelet count \>= 50 x 10\^9/L (without use of growth factors \[ie., interleukin 11 (oprelvekin)\]) * Prothrombin time (PT)/international normalized ratio (INR) =\< 2.3 or PT =\< 6 seconds above control * NOTE: Abnormal PT/INR may be considered, with documented principal investigator (PI) approval, if it is due to the use of anticoagulants; for such patients, a normal PT/INR must be available from before the start of anticoagulation treatment * Renal * Calculated creatinine clearance (CrCl) or 24-hour urine CrCl \> 50 mL/min (Cockcroft-Gault formula will be used to calculate CrCl) * Hepatic * Serum bilirubin =\< 3 times the upper limit of normal (ULN) * Aspartate aminotransaminase (AST) and alanine aminotransaminase (ALT) =\< 5 times ULN * Serum electrolytes * Lipase =\< 1.5 times ULN * Amylase =\< 1.5 times ULN * Potassium, sodium, magnesium, and calcium (corrected for serum albumin) =\< grade 1 or within the institutional ranges of normal; if clinically appropriate, electrolytes may be corrected and values reassessed prior to enrollment * Females of childbearing potential (FOCBP), and non-sterilized males who are sexually active must agree to the use of two methods of contraception, with one method being highly effective and the other method being either highly effective or less effective; they must also refrain from egg and/or sperm cell donation and breastfeeding for 90 days after the final dose of investigational product(s) * FOCBP are defined as those who are not surgically sterile (ie, bilateral tubal ligation, bilateral oophorectomy, or complete hysterectomy) or postmenopausal (defined as 12 months with no menses without an alternative medical cause) * Women of childbearing potential (WOCBP) must agree to follow instructions for method(s) of contraception for the duration of treatment with nivolumab plus 5 half-lives of nivolumab (19 weeks) plus 30 days (duration of ovulatory cycle) for a total of 23 weeks post-treatment completion. * Men who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment with nivolumab plus 5 half-lives of the study drug (19 weeks) plus 90 days (duration of sperm turnover) for a total of 31 weeks post-treatment completion * FOCBP must have a negative pregnancy test within 7 days prior to registration * Note: FOCBP will have to have repeat pregnancy test within 24 hours of starting nivolumab, scheduled for cycle 1 day 1 * Subjects must provide archived tumor specimens for correlative biomarker studies if sufficient tissue is available; a fresh biopsy is not required * Patients must have the ability to understand and the willingness to sign a written informed consent prior to registration on study Exclusion Criteria: * Patients must not have had prior treatment with nivolumab or any other PDL1 or PD-1 antagonists * Patients must not have a history of severe allergic reactions (i.e., grade 4 allergy, anaphylactic reaction from which the subject did not recover within 6 hours of institution of supportive care) to any unknown allergens or any components of the nivolumab formulations * Patients diagnosed or treated for malignancy other than HCC are not eligible unless they meet one of the following exceptions: * Malignancy treated with curative intent and with no known active disease present for \>= 3 years before registration and felt to be at low risk for recurrence by the treating physician. * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease. * Adequately treated cervical carcinoma in situ without evidence of disease * 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 chronic prolonged systemic corticosteroids (defined as corticosteroid use of duration one month or greater), 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 (IBD) * Crohn's * Ulcerative colitis * Patients with a history of toxic epidermal necrolysis (TEN) * Stevens-Johnson syndrome * Anti-phospholipid syndrome * NOTE: Subjects with 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 are permitted to enroll * Patients with renal failure currently requiring dialysis of any kind are not eligible * Patients with untreated central nervous system (CNS) metastatic disease (including spinal cord and leptomeningeal disease) are excluded * Note: Subjects with previously treated CNS metastases that are radiographically and neurologically stable for at least 6 weeks and do not require corticosteroids (of any dose) for symptomatic management are permitted to enroll * Concurrent enrollment in another clinical study, unless it is an observational (non-interventional) clinical study or the follow-up period of an interventional study, is excluded * Receipt of any investigational therapy is not permitted within 28 days prior to the first dose of nivolumab * Any concurrent chemotherapy, biologic or hormonal therapy for cancer treatment is not permitted within 28 days of registration * Note: Prior immunotherapy is not permitted * Note: Concurrent use of hormones for non-cancer-related conditions (e.g., insulin for diabetes and hormone replacement therapy) is acceptable * Patients with exposure to prior immunotherapy are not eligible * Patients are ineligible if they have unresolved toxicities from prior anticancer therapy, defined as having not resolved to National Cancer Institute (NCI) CTCAE version 4.03 grade 0 or 1 with the exception of alopecia and laboratory values listed per the inclusion criteria * Note: Subjects with irreversible toxicity that is not reasonably expected to be exacerbated by any of the investigational products may be included (eg, hearing loss) after consultation with the PI and Northwestern University (NU) Quality Assurance Monitor (QAM) * Radiation therapy is not permitted within 14 days of registration * Live vaccines are not permitted within 28 days of study registration * No systemic glucocorticoids will be permitted within 48 hours prior to study registration * Note: Topical steroids, bronchodilators and local steroid injections are permitted if clinically required * Patients with cardiac disease defined as one of the following are not eligible: * Congestive heart failure \> class II New York Heart Association (NYHA) * Unstable angina (anginal symptoms at rest) or new onset angina (began within the last 3 months) * Myocardial infarction within the past 6 months * Patients with cardiac ventricular arrhythmias requiring anti-arrhythmic therapy are not eligible * Patients with known human immunodeficiency virus (HIV) infection are not eligible * Patients must not have elevated lung shunting precluding treatment with Y-90 * Patients who have had major surgery within 4 weeks prior to registration are not eligible * Patients who have active clinically serious infection \> CTCAE grade 2 are not eligible * Patients with a history of gastrointestinal bleeding (GIB) within 6 weeks prior to registration are not eligible * Patients with prior transplant of any kind are not eligible * Known or suspected allergy to nivolumab or any agent given in the course of this trial is not permitted * Patients may not be pregnant or lactating at study registration * Patients who have an uncontrolled intercurrent illness including, but not limited to any of the following, are not eligible: * Hypertension (defined as \> 150/90) that is not controlled on medication * Ongoing or active infection requiring systemic treatment * Cardiac arrhythmia * Psychiatric illness/social situations that would limit compliance with study requirements * Any other illness or condition that the treating investigator feels would interfere with study compliance or would compromise the patient's safety or study endpoints * Active alcohol use, drug use, or a psychiatric disease that would, in the opinion of the PI or a sub-investigator (sub-I), prevent the subject from complying with the study protocol and/or endanger the subject during their participation in the study