Pembrolizumab (MK-3475) in Hepatocellular Carcinoma

Inclusion Criteria: * FOR ARM 1 AND 2: Subjects with advanced hepatocellular carcinoma (HCC) with no curative option; for Arm 2 subjects that are HCV-positive with genotype 1 or 4 virus infection will be enrolled * Be willing and able to provide written informed consent for the trial; the subject may also provide consent for Future Biomedical Research (FBR); however, the subject may participate in the main trial without participating in FBR. * Have histologically or cytologically documented HCC (documentation of original biopsy for diagnosis is acceptable if tumor tissue is unavailable) or clinical diagnosis by American Association for the Study of Liver Diseases (AASLD) criteria in cirrhotic subjects is required; for subjects without cirrhosis histological confirmation is mandatory * FOR ARM A AND B: Have Barcelona Clinic Liver Cancer (BCLC) stage C disease or BCLC stage B disease not amenable to locoregional therapy or refractory to locoregional therapy, and not amenable to a curative treatment approach * Have a Child-Pugh A liver score at screening or within 14 days of first dose of study drug * Have a predicted life expectancy of greater than 3 months * Have measurable disease based on RECIST 1.1 as confirmed by the blinded MD Anderson radiology; target lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions; Note: the same image acquisition and processing parameters should be used throughout the study for a given subject * Have a performance status of 0 or 1 using the Eastern Cooperative Oncology Group (ECOG) performance scale within 7 days of first dose of study drug * Have documented objective radiographic progression after stopping treatment with sorafenib or else intolerance to sorafenib; intolerance to sorafenib is defined as: Common Terminology Criteria for Adverse Events (CTCAE) grade \>= 2 drug-related adverse event(s) which both a) persisted in spite of comprehensive supportive therapy according to institutional standards and b) persisted or recurred after sorafenib treatment interruption of at least 7 days and dose reduction by one dose level; patients treated on sorafenib as the last treatment may start pembrolizumab at least 14 days after the last dose of sorafenib * FOR ARM B: Subjects with chronic infection by HCV who are treated or untreated are allowed on study; subjects with a past or resolved hepatitis B virus (HBV) infection, defined as having a negative hepatitis B surface antigen (HBsAg) test and a positive total hepatitis B core antibody (HBcAb) test and negative HBV deoxyribonucleic acid (DNA) test at screening, are eligible for the study * Have a negative urine or serum pregnancy test within 72 hours prior to receiving the first dose of study medication (cycle 1, day 1) (female subjects of childbearing potential); if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Be willing to use an adequate method of contraception for the course of the study through 120 days (Arm A) or 180 days (Arm B) after the last dose of study medication (male and female subjects of childbearing potential; acceptable methods of contraception are as follows: A) single method (one of the following is acceptable): a) intrauterine device (IUD); b) vasectomy of a female subject's male partner; c) contraceptive rod implanted into the skin B) combination method (requires use of two of the following): a) diaphragm with spermicide (cannot be used in conjunction with cervical cap/spermicide); c) cervical cap with spermicide (nulliparous women only); d) contraceptive sponge (nulliparous women only); e) male condom or female condom (cannot be used together); f) hormonal contraceptive: oral contraceptive pill (estrogen/progestin pill or progestin-only pill), contraceptive skin patch, vaginal contraceptive ring, or subcutaneous contraceptive injection; abstinence (relative to heterosexual activity) can be used as the sole method of contraception if it is consistently employed as the subject's preferred and usual lifestyle and if considered acceptable by local regulatory agencies and Ethical Review Committees (ERCs)/Institutional Review Boards (IRBs); periodic abstinence (e.g., calendar, ovulation, sympto-thermal, post-ovulation methods, etc.) and withdrawal are not acceptable methods of contraception; if a contraceptive method listed above is restricted by local regulations/guidelines, then it does not qualify as an acceptable method of contraception for subjects participating at sites in this country/region * Absolute neutrophil count \>= 1200/uL performed within 7 days of treatment initiation * Platelets \>= 60,000/uL performed within 7 days of treatment initiation * Hemoglobin \>= 8 g/dL without transfusion or erythropoietin (EPO) dependency within 7 days performed within 7 days of treatment initiation * Creatinine OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance) =\< 1.5 x upper limit of normal (ULN) OR \>= 60 mL/min for subject with creatinine levels \> 1.5 x institutional ULN; Note: creatinine clearance should be calculated per institutional standard performed within 7 days of treatment initiation * Total bilirubin =\< 2 mg/dL, or direct bilirubin =\< ULN for those with total bilirubin \> 2 x ULN performed within 7 days of treatment initiation * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 5 x ULN performed within 7 days of treatment initiation * Albumin \>= 3 g/dL performed within 7 days of treatment initiation * International normalized ration (INR) or prothrombin time (PT) activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants performed within 7 days of treatment initiation * FOR ARM B: Have a detectable GT1, GT4, or HCV viral load TD(q) based on the Roche COBAS AmpliPrep/COBAS TaqMan HCV Test, version (v)2.0 from a blood sample; HCV RNA (10,000 IU/mL in peripheral blood) at the time of screening have documented chronic HCV GT1, GT4 (with no evidence of mixed genotype) infection: a. Positive for anti-HCV antibody, HCV RNA, or any of the above HCV GTs at least 3 months before screening (HCV RNA and HCV GT must be confirmed by screening lab results) OR b. Positive for anti-HCV antibody or HCV RNA at the time of screening with a liver biopsy consistent with chronic HCV infection (or a liver biopsy performed before enrollment with evidence of chronic hepatitis C (CHC) disease, such as the presence of fibrosis) or a Fibroscan performed within 12 months of day 1 of this study with a result of \> 12.5 kPa or a FibroSure (Fibrotest) performed during Screening with a score of \> 0.75 and an aspartate aminotransferase (AST): platelet ratio index (APRI) of \> 2 * FOR ARM B: Subjects must undergo at screening HCV GT1a testing for resistance polymorphism as per Zepatier labe * FOR ARM B: Have liver disease staging assessment as follows: Cirrhosis is defined as any one of the following: a. A liver biopsy performed prior to day 1 of this study showing cirrhosis (F4) b. Fibroscan performed within 12 calendar months of day 1 of this study showing cirrhosis with result \> 12.5 kPa \[29\] c. A FibroSure (Fibrotest) performed during screening with a score of \> 0.75 and an AST: platelet ratio index (APRI) of \> 2; absence of cirrhosis is defined as any one of the following: a. Liver biopsy performed within 24 months of day 1 of this study showing absence of cirrhosis b. Fibroscan performed within 12 months of Day 1 of this study with a result of =\< 12.5 kPa \[29\] c. A Fibrosure (Fibrotest) score of 0.48 and AST to Platelet Ratio Index (APRI) of =\< 1 during Screening Fibroscan cut-off of 12.5 kPa has a positive predictive value of 90% and a sensitivity of 95% for \>/= F3; based on box and whisker plot of interquartile distribution \> 12.5 kPa will exclude the majority of subjects with metavir F3 fibrosis; in the absence of a definitive diagnosis of presence or absence of cirrhosis by the above criteria, a liver biopsy is required; liver biopsy results supersede the results obtained by Fibroscan or Fibrosure * Subjecs in Arm B treated with ribavirin (RBV) must agree to double barrier birth control from day 1 to 6 months following last dose of study therapy or they are excluded from this trial Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy, herbal/complementary oral or IV medicine, or used an investigation device within 4 weeks of the first dose of treatment; subjects must also have recovered from associated therapy (i.e., to grade =\< 1 or baseline) and from adverse events due to any prior therapy * Has had esophageal or gastric variceal bleeding within the last 6 months; all subjects will be screened for esophageal varices, unless such screening has been performed in the past 12 months before first dose of treatment; if varices are present, they should be treated according to institutional standards before starting study treatment * Subjects with ALT \> 5 x ULN at day 1 are not eligible for enrollment * Subjects with total bilirubin \> 2.0 mg/dL at day 1 are not eligible for enrollment * Subjects with clinically apparent ascites or encephalopathy, or untreated varices are not eligible for enrollment * Portal vein invasion at the main portal branch (Vp4), inferior vena cava, or cardiac involvement of HCC based on imaging * Has had encephalopathy in the last 6 months; subjects on rifaximin or lactulose to control their encephalopathy are not allowed * Had a solid organ or hematologic transplant * Had prior systemic therapy for HCC other than sorafenib, or intercurrent local therapy to the liver tumor between sorafenib and study drug * Has active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs); replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment; the use of physiologic doses of corticosteroids may be approved after consultation with the sponsor * Has received locoregional therapy to liver (transarterial chemoembolization \[TACE\], transarterial embolization \[TAE\], radiation, radioembolization, or ablation) or surgery to liver or other site within 6 weeks prior to the first dose of study drug; minor surgery must have occurred at least 7 days prior to the first dose of study treatment (cycle 1, day 1); subjects must have recovered adequately (i.e., grade =\< 1 or baseline) from the toxicity and/or complications from any intervention prior to starting therapy * Has a known history of an additional malignancy, except if the participant has undergone potentially curative therapy with no evidence of that disease recurrence for 5 years since initiation of that therapy * Has radiographically detectable (even if asymptomatic and/or previously treated) central nervous system (CNS) metastases and/or carcinomatous meningitis as assessed by local site investigator and radiology review/CIV * Has a history of (non-infectious) pneumonitis that required steroids or there is current pneumonitis * Has an active infection requiring systemic therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator, including dialysis * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 120 days after the last dose of trial treatment * Has received prior immunotherapy including anti-PD-1, anti-PD-L1, or anti-PD-L2 agents, or if the subject has previously participated in Merck pembrolizumab clinical trials * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has untreated active hepatitis B; Note: to qualify for enrollment, antiviral therapy for HBV must be given for at least 3 months prior to first dose of study drug, and HBV viral load must be less than 100 IU/mL prior to first dose of study drug; those on active HBV therapy with viral loads under 100 IU/mL should stay on the same therapy throughout study treatment; those subjects who are anti-HBc (+) and negative for HBsAg, Anti-HBs, and HBV viral load do not require HBV prophylaxis, but need close monitoring for reactivation * Subjects who have received therapy for HCV =\< 4 weeks from the start of pembrolizumab; Note: those with untreated HCV and those who completed HCV therapy \>= 4 weeks of study treatment start are eligible * Has dual infection with HBV/HCV or other hepatitis combinations at study entry * Has received a live vaccine within 30 days of planned start of study therapy (cycle 1, day 1); Note: the killed virus vaccines used for seasonal influenza vaccines for injection are allowed; however intranasal influenza vaccines (e.g., FluMist) are live attenuated vaccines and are not allowed * Has received sorafenib within 14 days of first dose of study medication