Cabozantinib and Pembrolizumab for the First-Line Treatment of Advanced Liver Cancer

Inclusion Criteria: * Must have a histologically confirmed diagnosis of HCC or a non-invasive diagnosis of HCC as per the American Association for the Study of Liver Diseases (AASLD) criteria * If available, archival tissue must be submitted * Mixed HCC-cholangiocarcinoma is not allowed * Patient has Barcelona Clinic Liver Cancer (BCLC) stage C disease, or BCLC stage B disease that is not amenable to locoregional therapy or refractory to locoregional therapy, and not amenable to curative treatment * Previous locoregional therapy is allowed (e.g. surgical resection, external beam radiation, catheter-based therapy), and patients must have evidence of disease progression from locoregional therapy * Must have measurable disease by RECIST v1.1 * Lesions that were previously radiated or ablated cannot be target lesions unless there was subsequent radiographic progression at those sites * No prior systemic therapy for HCC. Prior chemotherapy given locally into the liver (e.g. transarterial chemoembolization \[TACE\]) is allowed * Must have Child-Pugh class A hepatic function within 7 days prior to first dose of study intervention * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Life expectancy of at least 12 weeks * Recovery to baseline or =\< grade 1 toxicities (CTCAE v5) related to any prior treatments, unless adverse events (AEs) are clinically nonsignificant and/or stable on supportive therapy * Absolute neutrophil count (ANC) \>= 1500/mm\^3 without granulocyte colony-stimulating factor support (within 14 days before first dose of study treatment) * Platelets \>= 60,000/mm\^3 without transfusion (within 14 days before first dose of study treatment) * Hemoglobin \>= 9 g/dL (\>= 90 g/L) without transfusion or erythropoietin (EPO) dependency (within 14 days before first dose of study treatment) * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 5 x upper limit of normal (ULN) (within 14 days before first dose of study treatment) * Total bilirubin =\< 2 mg/dL OR direct bilirubin =\< ULN for participants with total bilirubin levels \> 2 mg/dL (within 14 days before first dose of study treatment) * Serum albumin \>= 2.8 g/dl (\>= 28 g/L) without albumin infusion (within 14 days before first dose of study treatment) * Prothrombin time (PT)/international normalized ratio (INR) or partial thromboplastin time (PTT) test =\< 1.5 x ULN (within 14 days before first dose of study treatment) * Serum creatinine =\< 1.5 x ULN or calculated creatinine clearance \>= 40 mL/min using the Cockcroft-Gault equation (within 14 days before first dose of study treatment) * Urine protein/creatinine ratio (UPCR) =\< 1 mg/mg (=\< 113.2 mg/mmol) or 24 hour(h) urine protein =\< 1 g (within 14 days before first dose of study treatment) * Hemoglobin A1c (HbA1c) =\< 8% within 28 days before randomization or fasting serum glucose =\< 160 mg/dL (within 14 days before first dose of study treatment) * Patients with positive hepatitis B surface antigen (HBsAg) and/or hepatitis B virus (HBV) viral load \> 100 IU/mL at the time of enrollment are eligible to enroll on study if they meet the following criteria: * Anti-HBV therapy as per institutional practice must be given at least 4 weeks and HBV viral load must be \< 100 IU/mL prior to initiating study treatment. Patients on active HBV therapy with viral loads \< 100 IU/mL should remain on the same therapy throughout study treatment * Note: Patients with positive anti-hepatitis B core antibody (HBcAb), negative HBsAg, and negative or positive anti-hepatitis B surface antibody, and who have an HBV viral load \< 100 IU/mL do not require anti-viral prophylaxis * Patients with past or ongoing hepatitis C infection (HCV) are eligible to enroll on study, with or without prior anti-viral treatment, as long as the other eligibility criteria are met. Treated patients must have completed their anti-viral treatment at least 1 month prior to initiating study treatment * Sexually active fertile subjects and their partners must agree to use effective methods of contraception during the course of the study and for at least 4 months after the last dose cabozantinib. They must also refrain from donating sperm during this time period * Female subjects of childbearing potential must not be pregnant at screening and not breastfeeding. Females of childbearing potential are defined as premenopausal females capable of becoming pregnant (i.e. females who have had any evidence of menses in the past 12 months, with the exception of those who had prior hysterectomy) * Women who have been amenorrheic for 12 or more months are still considered to be of childbearing potential if the amenorrhea is possibly due to prior chemotherapy, antiestrogens, low body weight, ovarian suppression or other reasons * Capable of understanding and complying with the protocol requirements and must provide written informed consent/assent for the study Exclusion Criteria: * Prior treatment with any systemic therapy for HCC, including anti-VEGF therapy or any systemic investigational agent * If the patient previously received systemic treatment for reasons other than HCC: small molecule kinase inhibitors are not allowed within 2 weeks and cytotoxic/biologic agents are not allowed within 4 weeks of study treatment * Prior exposure to immune checkpoint inhibitors or other immunotherapeutic agents * Currently participating in or has participated in a study of an investigational agent or device within 4 weeks prior to the first dose of study treatment * Major surgery within 6 weeks or minor surgery (e.g. dental extraction) within 10 days prior to first dose of study treatment * Complete wound healing from major surgery must have occurred at least 1 month before first dose and from minor surgery (e.g. simple excision, tooth extraction) at least 7 days before first dose. Subjects with clinically relevant ongoing complications from prior surgery are not eligible * Local liver-directed therapy within 4 weeks of initiating study treatment * Palliative radiation for the purpose of symptomatic relief to non-liver and non-central nervous system (CNS) disease within 2 weeks of starting treatment. Other radiation treatments within 4 weeks of starting treatment * Patients must have recovered from all radiation-related toxicities, not require corticosteroids, and have not had radiation pneumonitis * Prior liver or other allogenic tissue/organ transplantation * History of primary immunodeficiency * Active autoimmune or inflammatory disease that has required systemic treatment in the past 2 years (i.e. with use of disease-modifying agents, corticosteroids or immunosuppressive drugs). This includes, but is not limited to, inflammatory bowel disease, celiac disease, systemic lupus erythematosus, rheumatoid arthritis, myasthenia gravis, Graves' disease, etc. * The following autoimmune conditions are allowed: vitiligo or alopecia; hypothyroidism on stable hormone replacement therapy; psoriasis/eczema not requiring systemic treatment * Replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed * Chronic use of systemic steroid (in dosing exceeding 10 mg daily of prednisone equivalent) or immunosuppressive therapy or use within 14 days prior to enrollment * The following treatments are allowed: intranasal, inhaled, topical or local steroid injections; systemic corticosteroids at physiologic doses equivalent to no more than prednisone 10 mg/day; steroids as premedication for contrast dye allergy * History of (non-infectious) pneumonitis that required steroids or has current pneumonitis * History of hepatic encephalopathy or treatment to prevent or control encephalopathy within the past 12 months. Subjects on lactulose and/or rifaximin to control hepatic encephalopathy are not allowed * Esophageal or gastric variceal bleeding within the past 6 months. All subjects will be screened for esophageal varices unless performed in the last 6 months before study treatment. If varices are present, they should be treated according to institutional standards before starting study treatment * Uncontrolled ascites, clinically significant or symptomatic ascites requiring paracenteses or increasing doses of diuretics within the past 3 months * Patients who are on stable diuretic doses for at least 3 months are eligible if they meet other eligibility criteria * Asymptomatic ascites detected on imaging are allowed * Has known history or any evidence of CNS metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are asymptomatic and radiologically stable (i.e. without progression for at least 4 weeks by repeat imaging \[which must be performed during study screening\], clinically stable, and without the need steroids for at least 4 weeks prior to first dose of study treatment) * Concomitant anticoagulation with oral anticoagulants (e.g. warfarin, direct thrombin and factor Xa inhibitors) or platelet inhibitors (e.g. clopidogrel). Allowed anticoagulants are the following: * Low-dose aspirin for cardioprotection (per local applicable guidelines) is permitted * Low molecular weight heparin (LMWH) is permitted * Anticoagulation with therapeutic doses of LMWH is allowed in subjects without known brain metastases who are on a stable dose of LMWH for at least 4 weeks before first dose of study treatment, and who have had no clinically significant hemorrhagic complications from the anticoagulation regimen or the tumor * The subject has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: * Cardiovascular disorders: * Congestive heart failure New York Heart Association class 3 or 4, unstable angina pectoris, serious cardiac arrhythmias with risk of hemodynamic instability within 12 months before the first dose of study treatment * Uncontrolled hypertension defined as sustained blood pressure (BP) \> 150 mm Hg systolic or \> 95 mm Hg diastolic despite optimal antihypertensive treatment, and/or change in antihypertensive medications within 1 week before starting treatment. Note: eligibility of a subject receiving 4 or more antihypertensive medications prior to study entry will require approval from the principal investigator (PI) * Stroke (including transient ischemic attack \[TIA\]), myocardial infarction (MI), or other ischemic event, or arterial thromboembolic within 12 months before the first dose * Asymptomatic venous thromboembolic event (e.g. deep venous thrombosis, pulmonary embolism) is allowed if the patient has been stable on anticoagulation with LMWH for at least 4 weeks * Gastrointestinal (GI) disorders including those associated with a high risk of perforation or fistula formation: * The subject has evidence of tumor invading the GI tract, active peptic ulcer disease, inflammatory bowel disease (e.g. Crohn's disease), GI malabsorption, diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis, acute pancreatitis, acute obstruction of the pancreatic duct or common bile duct, or gastric outlet obstruction * Abdominal fistula, GI perforation, bowel obstruction, or intra-abdominal abscess within 6 months before first dose * Note: Complete healing of an intra-abdominal abscess must be confirmed before first dose * Clinically significant hematuria, hematemesis, or hemoptysis of \> 0.5 teaspoon (2.5 ml) of red blood, other history of significant bleeding (e.g. pulmonary hemorrhage) within 12 weeks before first dose, or known thrombotic disorder * Cavitating pulmonary lesion(s) or known endotracheal or endobronchial disease manifestation * Lesions invading any major blood vessels, including main portal vein, inferior vena cava, or cardiac involvement of HCC based on imaging * Note: Main and branch portal vein and hepatic vein invasion is allowed * Ongoing active infection requiring antibiotics. Antibiotics must be completed at least 7 days before initiating study treatment * Known active tuberculosis * Serious non-healing wound, ulcer, or bone fracture * Patients with proteinuria \> 1+ on urine dipstick testing will undergo 24-hour urine collection for quantitative assessment of proteinuria. Participants with urine protein \>= 1 g/24 hours will be ineligible * Corrected QT interval calculated by the Fridericia formula (QTcF) \> 480 ms per electrocardiogram (EKG) within 28 days before first dose of study treatment * Note: If a single EKG shows a QTcF with an absolute value \> 500 ms, two additional EKGs at intervals of approximately 3 min must be performed within 30 min after the initial EKG, and the average of these three consecutive results for QTcF will be used to determine eligibility * Inability to swallow tablets or any other condition that might interfere with oral absorption of medications * Previously identified allergy or hypersensitivity to study drugs and/or any of their excipients * Ongoing secondary malignancy that is progressing and/or has required active treatment within the past year. Adjuvant treatment for resected breast cancer is allowed * Subjects with basal cell carcinoma of the skin, squamous cell carcinoma or the skin, or carcinoma in situ (e.g. breast carcinoma, cervical cancer in situ) that have undergone potentially therapy are allowed * Has a known history of human immunodeficiency virus (HIV) infection. Note: HIV testing is not mandated for screening * Co-infection with HBV (HBsAg \[+\] and /or detectable HBV DNA) and HCV (anti-HCV Ab \[+\] and detectable HCV ribonucleic acid \[RNA\]) at study entry * Co-infection with HBV and hepatitis D virus (HDV) at study entry * Live attenuated vaccine within 30 days prior to first dose of study treatment. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g. FluMist) are live attenuated vaccines and are not allowed * Pregnant or lactating females * Known psychiatric illness, substance abuse disorder, or other condition that would interfere with the ability to comply with the requirements of the study * Has history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator