Cryoablation and Arterial Infusion of SD-101 in Combination with Durvalumab and Tremelimumab

Inclusion Criteria: * Willing and able to provide written informed consent prior to performance of any study- specific procedures. * Age ≥ 18 years. * Locally advanced or metastatic and/or unresectable hepatocellular carcinoma (HCC) with diagnosis confirmed by histology/cytology or clinically by American Association for the Study of Liver Diseases (AASLD) criteria in cirrhotic participants: 1. For cirrhotic participants with no histological confirmation of diagnosis, clinical confirmation is required per AASLD criteria. 2. Pathological diagnoses of HCC will be made according to the International Working Party criteria. * HCC with a component that measures at least 3 cm and that is located 1 cm or greater away from sensitive structures, including large blood vessels, large bile ducts, pericardium, diaphragm, gallbladder, stomach, and bowel. * Is not a candidate for local therapies alone, including liver transplantation, tumor ablation, transarterial embolization, radiation therapy, or resection. * No prior systemic therapy for advanced or metastatic HCC. * Eastern Cooperative Oncology Group (ECOG) Performance Status ≤ 1 * Evaluable target lesions as per Response Evaluation Criteria in Solid Tumors RECIST v1.1 or mRECIST. * Child-Pugh A or Child-Pugh B7 liver function. * Life expectancy of ≥ 12 weeks. * Adequate bone marrow function defined as: 1. Peripheral absolute neutrophil count ≥ 1000/mm\^3 2. Platelet count ≥ 50,000/ mm\^3 3. Hemoglobin ≥ 8.0 g/dL * Adequate renal function defined as creatinine clearance ≥ 50 ml/min * Adequate liver and pancreatic function defined as: 1. Total bilirubin ≤ 2.0 x institution's upper limit of normal, and 2. Alanine transaminase (ALT) or Aspartate transaminase (AST) ≤ 5 x institution's upper limit of normal, and 3. Albumin ≥ 2 g/dL * Adequate central nervous system function defined as: a. patients with seizure disorder may be enrolled if on anticonvulsants and seizures are well controlled. * Systolic blood pressure \<160 mm Hg. * Patients with partners of childbearing potential must agree to use adequate contraception during participation in the study. * Patients able to become pregnant are eligible to enter the study if they are either: 1. Of non-childbearing potential (i.e., physiologically incapable of becoming pregnant), including: i. Has had a hysterectomy; or ii. Has had a bilateral oophorectomy, or iii. Has had a bilateral tubal ligation, or iv. Is post-menopausal (demonstrates total cessation of menses for greater than or equal to 1 year); OR 2. Of childbearing potential, has a negative serum pregnancy test at screening, and agrees to one of the following contraceptives: i. An intrauterine device with a documented failure rate of less than 1% per year; ii. Vasectomized partner who is sterile prior to the subject's entry and is the sole sexual partner for that woman; iii. Complete abstinence from sexual intercourse for 14 days before exposure to investigational product, during the clinical trial, and for at least 14 days after the last dose of investigational product; iv. Double barrier contraception defined as condom with spermicidal jelly, foam, suppository, or film; OR diaphragm with spermicide; OR male condom and diaphragm. Exclusion Criteria: * Brain metastases or spinal cord compression, unless treatment was completed at least 4 weeks before study entry, and stable without steroid treatment for at least 4 weeks. * Evidence of severe or uncontrolled systemic diseases \[e.g., unstable or uncompensated respiratory, cardiac (including life threatening arrhythmias)\]. * Unresolved toxicity ≥ CTCAE Grade 2 from previous anti-cancer therapy except alopecia (if applicable) unless agreed that the patient can be entered after discussion with the Medical Monitor. * Presence of cardiac impairment defined as: 1. prior history of cardiovascular disease including heart failure that meets New York Heart Association (NYHA) class III and IV definitions; OR 2. history of myocardial infarction/active ischemic heart disease within one year of study entry; OR 3. uncontrolled dysrhythmias; OR 4. poorly controlled angina * Participation in a trial of an investigational agent within the prior 30 days * Pregnant or breast-feeding. * High volume peritoneal or pleural effusions requiring centesis more frequently than every 14 days. * Poorly controlled or refractory (grade 3-4) hepatic encephalopathy. * History of allogeneic stem cell or solid organ transplantation. * Prior history of pneumonitis/interstitial lung disease. * Receipt of live vaccine within 30 days. * Active or prior documented autoimmune or inflammatory disorders (including but not limited to myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjögren syndrome, Guillain-Barré syndrome, multiple sclerosis). The following are exceptions to this criterion: 1. Vitiligo or alopecia. 2. Autoimmune-related hypothyroidism stable on thyroid replacement therapy. 3. Any chronic skin condition that does not require systemic therapy. 4. Controlled type 1 diabetes mellitus who are on an insulin regimen. 5. Celiac disease controlled by diet alone. 6. Without active disease in the last 5 year. * Current or prior use of immunosuppressive medication within 14 days before the first dose of durvalumab. The following are exceptions to this criterion: 1. Intranasal, inhaled, topical steroids, or local steroid injections (e.g. intra-articular injection). 2. Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or its equivalent. 3. Steroids as premedication for hypersensitivity reactions (e.g. CT scan premedication) * Any concurrent condition that, in the investigator's opinion, makes it undesirable for the patient to participate in the trial or which would jeopardize compliance with the protocol.