Durvalumab With/Without Tremelimumab After Palliative Hypofractionated Radiotherapy for Hepatocellular Carcinoma

Inclusion Criteria: 1. Histologically-diagnosed HCC with progression during or after prior PD-(L)1 checkpoint inhibitor immunotherapy (e.g., nivolumab and/or pembrolizumab or atezolizumab; prior durvalumab excluded), or without prior PD-(L)1 checkpoint inhibitor immunotherapy. a. For patients without prior histologic or cytologic diagnosis, radiographic diagnosis is allowed provided patients meet American Association for the Study of Liver Diseases (AASLD) criteria for radiographic diagnosis. 2. At least 1 Response Evaluation Criteria in Solid Tumors (RECIST) 1.1-measurable tumor present which has not received RT or other local therapy prior to enrollment. 3. Clinical indication for RT to any site (e.g. painful primary or metastatic tumor, local complication risk such as impending biliary or vascular obstruction). 4. Child Pugh score of A, B7, or B8 provided other liver function criteria are met. 5. Eastern Cooperative Oncology Group (ECOG) 0 or 1 6. Appropriate antiviral therapy for hepatitis B virus (HBV) according to institutional standard of care with HBV deoxyribonucleic acid (DNA) polymerase chain reaction (PCR) \< 2000 IU/mL. 7. Adequate organ function as defined below: * Hemoglobin \>= 9.0 g/dL * Absolute neutrophil count \>= 1,200/microliter (mcL) * Platelet count \>= 60,000/mcL * Serum bilirubin =\< 1.5 x institutional upper limit of normal. 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) =\< 2.5 x institutional upper limit of normal unless liver metastases are present in which case it can be =\< 5 x upper limit of normal (ULN) * International normalized ratio (INR) \< 1.5 * Creatinine clearance \> 30 mL/min by Cockcroft Gault formula. 8. No contraindication to immune checkpoint inhibitor immunotherapy. 9. No contraindication to RT. 10. Age \>=18 years at time of study entry. 11. Life expectancy of \>= 12 weeks. 12. Body weight \> 30 kg (66.1 pounds). 13. 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) 14. Women of childbearing potential and men must agree to use adequate contraception from the time of screening through the duration of study participation and for at least 6 months after receiving combination of durvalumab plus tremelimumab and 3 months after last dose of durvalumab. 15. 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. 16. 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. Exclusion Criteria: 1. Prior radiotherapy to tumor sites requiring RT which could compromise safety of additional treatments. 2. Prior radiotherapy to more than 30% of bone marrow or to a wide field within 4 weeks of the first study treatment. 3. Prior treatment with cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) or PD-L1 inhibitor. 4. History of allogenic organ transplantation. 5. On prior PD-1 inhibitor immunotherapy: * Any immune-related adverse events with National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version (v) 5 grade \>= 3 on any prior immunotherapy or toxicity that led to permanent discontinuation of prior immunotherapy. * Any AEs while receiving prior immunotherapy not resolved to grade =\< 1 or resolved to baseline, with the exception of patients with endocrine AE of grade =\< 2, who are permitted to enroll if they are stably maintained on appropriate replacement therapy and are asymptomatic * Required the use of additional immunosuppression other than corticosteroids for the management of an AE, experienced recurrence of a grade \>= 3 AE if previously re-challenged, and currently require maintenance doses of \> 10 mg prednisone or equivalent per day 6. Major surgery, liver-directed therapy, or any other anticancer therapy (e.g. chemotherapy, immunotherapy, endocrine therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal antibodies) less than 4 weeks prior to enrollment 7. Any other unresolved toxicity NCI 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 or tremelimumab may be included only after consultation with the study physician 8. Concurrent enrollment in another interventional clinical study, except only in the follow-up period of that study. 9. Participation in another interventional clinical study with an investigational product during the past 4 weeks except only in the follow-up period of that study. 10. 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 with celiac disease controlled by diet alone * Patients without active disease in the last 5 years may be included but only after consultation with the study physician 11. 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 AEs or compromise the ability of the patient to give written informed consent 12. History of another primary malignancy except for: * Malignancy treated with curative intent and with no known active disease \>= 2 years before the first dose of investigational product (IP) 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 13. History of leptomeningeal carcinomatosis. 14. History of active primary immunodeficiency. 15. Active infection including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and tuberculosis (TB) testing in line with local practice). 16. Known human immunodeficiency virus (HIV) infection. 17. Current or prior use of immunosuppressive medication within 14 days before the first dose of durvalumab/tremelimumab. The following are exceptions to this criterion: * Intranasal, inhaled, topical steroids, 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) 18. Receipt of live attenuated vaccine within 30 days prior to the first dose of IP. Note: Patients, if enrolled, should not receive live vaccine whilst receiving IP and up to 30 days after the last dose of IP. 19. 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 through the duration of study participation and for at least 6 months after receiving combination of durvalumab plus tremelimumab and 3 months after last dose of durvalumab. 20. Known allergy or hypersensitivity to IP, any of the study drugs, or any of the study drug excipients. 21. Prior randomization or treatment in a previous durvalumab and/or tremelimumab clinical study regardless of treatment arm assignment. 22. Involvement in the planning and/or conduct of the study (applies to both AstraZeneca staff and/or staff at the study site). 23. Any condition which, in the investigator's opinion, makes the subject unsuitable for trial participation.