• Patients, or their legal guardian, must give written informed consent prior to initiation of therapy, and patients under age 18 must give assent in keeping with the policies of the institution. Patients with a history of major psychiatric illness must be judged able to fully understand the investigational nature of the study and the risks associated with the therapy

• Patients with histologically confirmed FLHCC (or with documentation of original biopsy for diagnosis is acceptable if tumor tissue is unavailable). The determination of resectability status will ultimately lie in the clinical judgment of the surgical oncologist and medical oncologist involved in the care of the patient. The definition of resectability is as follows: hepatectomy can achieve a negative margin while preserving more than 30% of the total estimated liver volume, sparing two contiguous hepatic segments, and maintaining vascular inflow, vascular outflow, and biliary drainage. Patients with extrahepatic disease are defined as having unresectable disease

• Patient must have measurable disease defined as a lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) and measures \>= 15 mm with conventional techniques or \>= 10 mm with more sensitive techniques such as magnetic resonance imaging (MRI) or spiral computed tomography (CT) scan

• Eastern Cooperative Oncology Group performance status (ECOG PS =\< 1), or for patients under age 18 Karnofsky performance status of \>= 70

• No advanced cirrhosis, with Child-Pugh A

• Absolute neutrophil count (ANC) \>= 1,000 /mm\^3 (within 14 days of the first dose of study drug)

• Platelets \>= 100,000 /mm\^3 (within 14 days of the first dose of study drug)

• Hemoglobin \> 9.0 g/dL (may be transfused or receive epoetin alfa \[e.g., Epogen\] to maintain or exceed this level) (within 14 days of the first dose of study drug)

• Total bilirubin =\< 1.5 mg/dL (within 14 days of the first dose of study drug)

• Serum creatinine =\< 1.5 times the upper limit of normal (ULN) or estimated creatinine clearance (CrCL) \> 40 mL/min (within 14 days of the first dose of study drug)

• Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and/or alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 5 times institutional ULN (within 14 days of the first dose of study drug)

• Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin) within 24 hours prior to the start of study drug

• Women must not be breastfeeding

• WOCBP must agree to follow instructions for method(s) of contraception from the time of enrollment for the duration of treatment with study drug(s) plus 5 half-lives of study drug(s) plus 30 days (duration of ovulatory cycle) for a total of 5 months post treatment completion

• Men who are sexually active with WOCBP must agree to follow instructions for method(s) of contraception for the duration of treatment with study drug(s) plus 5 half-lives of study drug(s) plus 90 days (duration of sperm turnover) for a total of 7 months post-treatment completion

• Azoospermic males and WOCBP who are continuously not heterosexually active are exempt from contraceptive requirements. However, WOCBP must still undergo pregnancy testing as described in these sections. Investigators shall counsel WOCBP and male subjects who are sexually active with WOCBP on the importance of pregnancy prevention and the implications of an unexpected pregnancy. Investigators shall advise WOCBP and male subjects who are sexually active with WOCBP on the use of highly effective methods of contraception, which have a failure rate of \< 1% per year when used consistently and correctly. At a minimum, subjects must agree to the use of two methods of contraception, with one method being highly effective and the other method being either highly effective or less effective as listed below:

‣ HIGHLY EFFECTIVE METHODS OF CONTRACEPTION:

• Male condoms with spermicide

∙ Hormonal methods of contraception including combined oral contraceptive pills, vaginal ring, injectables, implants, and intrauterine devices such as Mirena by WOCBP subject or male subject's WOCBP partner

∙ Nonhormonal intrauterine devices, such as ParaGard

∙ Tubal ligation

∙ Vasectomy

∙ Complete Abstinence

⁃ Complete abstinence is defined as complete avoidance of heterosexual intercourse and is an acceptable form of contraception for all study drugs. Abstinence is only acceptable when this is in line with the preferred and usual lifestyle of the subject. Periodic abstinence (e.g., calendar, ovulation, symptothermal, profession of abstinence for entry into a clinical trial, post-ovulation methods) and withdrawal are not acceptable methods of contraception. Subjects who choose complete abstinence are not required to use a second method of contraception, but female subjects must continue to have pregnancy tests. Acceptable alternate methods of highly effective contraception must be discussed in the event that the subject chooses to forego complete abstinence

⁃ LESS EFFECTIVE METHODS OF CONTRACEPTION:

• Diaphragm with spermicide

∙ Cervical cap with spermicide

∙ Vaginal sponge

∙ Male condom without spermicide

∙ Progestin-only pills by WOCBP subject or male subject's WOCBP partner

∙ Female condom

⁃ A male and female condom must not be used together