Durvalumab and Tremelimumab After Radioembolization for the Treatment of Unresectable, Locally Advanced Liver Cancer

Inclusion Criteria: * Patients with histologically or cytologically confirmed unresectable, locally advanced hepatocellular carcinoma as defined by Barcelona Clinic Liver Cancer (BCLC) (B) intermediate stage or BCLC (C) advanced stage without extra-hepatic disease (only with branch portal vein thrombosis) * Capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in this protocol. Written informed consent and any locally required authorization (e.g., Health Insurance Portability and Accountability Act in the United States \[US\]) obtained from the patient/legal representative prior to performing any protocol-related procedures, including screening evaluations * Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up * Eastern Cooperative Oncology Group (ECOG) 0-1 * Must have a life expectancy of at least 12 weeks * Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply: * Women \< 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy) * Women \>= 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses \> 1 year ago, had chemotherapy-induced menopause with last menses \> 1 year ago, or underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy or hysterectomy) * Male patients must be surgically sterile, or if sexually active and having a pre-menopausal female partner then must be using an acceptable form of contraception * Have a Child-Pugh class A liver score within 7 days of radioembolization * 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) as outlined in RECIST version 1.1 * Patients should have been identified by their respective physicians as candidates for radioembolization * Body weight \> 30 kg * Subjects with chronic infection by hepatitis C virus (HCV) who are untreated are allowed on study. In addition, subjects with successful HCV treatment (defined as sustained virologic response \[SVR\] 12 or SVR 24) are allowed as long as 4 weeks have passed between completion of HCV therapy and start of study drug * Subjects with hepatitis B virus (HBV) may only be enrolled if their hepatitis is judged clinically stable by the investigator * Hemoglobin \>= 9.0 g/dL * Absolute neutrophil count (ANC) \>= 1500/uL * Platelet count \>= 75000/uL * Total bilirubin \< 2.0 mg/dL. This will not apply to patients with confirmed Gilbert's syndrome (persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis or hepatic pathology), who will be allowed only in consultation with their physician * Aspartate aminotransferase (AST/serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT/serum glutamate pyruvate transaminase \[SGPT\]) =\< 5 x upper limit of normal (ULN) * Albumin \>= 2.8 g/dL * International normalized ration =\< 1.6 * Measured creatinine clearance (CL) \> 40 mL/min or calculated creatinine CL \> 40 mL/min by the Cockcroft-Gault formula (Cockcroft and Gault 1976) or by 24-hour urine collection for determination of creatinine clearance Exclusion Criteria: * Portal vein invasion at the main portal branch (Vp4), inferior vena cava, or cardiac involvement of hepatocellular carcinoma (HCC) based on imaging. Vascular invasion to portal vein side branches are eligible for study * Evidence of diffuse HCC (tumor burden occupying \> 50% of liver) * Any evidence of known metastatic disease * Major surgical procedure (as defined by the investigator) within 28 days prior to radioembolization * Note: Local surgery of isolated lesions for palliative intent is acceptable * Participation in another clinical study with an investigational product during the last 4 weeks * Concurrent enrollment in another clinical study, unless it is an observational (non-interventional) clinical study or during the follow-up period of an interventional study * Receipt of the last dose of anticancer therapy (chemotherapy, immunotherapy, endocrine therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal antibodies) =\< 28 days prior to the first dose of study drug. If sufficient wash-out time has not occurred due to the schedule or pharmacokinetic (PK) properties of an agent, a longer wash-out period will be required, as agreed by AstraZeneca/MedImmune and the investigator * Prior exposure to anti-PD-1/PD-L1 inhibitor or anti-CTLA4 inhibitor, including durvalumab or tremelimumab * Any unresolved toxicity National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) grade \>= 2 from previous anticancer therapy with the exception of alopecia, vitiligo, and the laboratory values defined in the inclusion criteria * Patients with grade \>= 2 neuropathy will be evaluated on a case-by-case basis after consultation with the study physician * Patients with irreversible toxicity not reasonably expected to be exacerbated by treatment with durvalumab and/or tremelimumab may be included only after consultation with the study physician * Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], diverticulitis \[with the exception of diverticulosis\], systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc\]). The following are exceptions to this criterion: * Patients with vitiligo or alopecia * Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement * Any chronic skin condition that does not require systemic therapy * Patients without active disease in the last 5 years may be included but only after consultation with the study physician * Patients with celiac disease controlled by diet alone * History of allogenic organ transplantation * Evidence of pulmonary lung shunt greater than 10% or expected lung dose of \> 30 Gy * Uncontrolled intercurrent illness, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, interstitial lung disease, serious chronic gastrointestinal conditions associated with diarrhea, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring adverse events (AEs) or compromise the ability of the patient to give written informed consent * History of another primary malignancy except for * Malignancy treated with curative intent and with no known active disease \>= 5 years before the first dose of study treatment and of low potential risk for recurrence * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease * Adequately treated carcinoma in situ without evidence of disease * History of active primary immunodeficiency * Receipt of live attenuated vaccine within 30 days prior to the first dose of study treatment * Note: Patients, if enrolled, should not receive live vaccine whilst receiving study treatment and up to 30 days after the last dose of study treatment * Active systemic infection including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and tuberculosis (TB) testing in line with local practice. Use of antibiotics to treat superficial infection or contamination of tumor shall not, by itself, be considered evidence of infection * History of leptomeningeal carcinomatosis * Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients * Any concurrent chemotherapy, investigational product (IP), biologic, or hormonal therapy for cancer treatment. Concurrent use of hormonal therapy for non-cancer-related conditions (e.g., hormone replacement therapy) is acceptable * Current or prior use of immunosuppressive medication within 14 days before the first dose of durvalumab or tremelimumab. The following are exceptions to this criterion: * Intranasal, inhaled, topical steroid or local steroid injections (e.g., intra articular injection) * Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or its equivalent * Steroids as premedication for hypersensitivity reactions (e.g., computed tomography \[CT\] scan premedication) * Female patients who are pregnant or breastfeeding or male or female patients of reproductive potential who are not willing to employ effective birth control from screening to 90 days after the last dose of durvalumab + tremelimumab combination therapy or 90 days after the last dose of durvalumab monotherapy, whichever is longer * Female subjects, unless postmenopausal or surgically sterile, unwillingness to practice effective contraception, as per investigator discretion during the study. The rhythm method is not to be used as the sole method of contraception * Male subjects, unwillingness to practice effective contraception (per investigator discretion) while taking part in this study, because the effects of the SIR-Spheres treatment on sperm or upon the development of an unborn child are unknown * Inability or unwillingness to understand or sign a written informed consent document * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)