Bevacizumab and Erlotinib in Treating Patients With Advanced Liver Cancer

Inclusion Criteria: * Absolute neutrophil count \>= 1,500/mm\^3 * Creatinine =\< 2 mg/dL * Albumin \>= 2.5 g/dL * Total bilirubin =\< upper limit of normal (ULN) * aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 times ULN * Alkaline phosphatase =\< 5 times ULN * Urine protein:creatinine ratio \< 1.0 OR 24-hour urine protein \< 1,000 mg * Not pregnant or nursing: No nursing for \>= 6 months after completion of study treatment * Negative pregnancy test * Fertile patients must use effective contraception during study and for \>= 6 months after completion of study treatment * No history of allergic reactions attributed to compounds of similar chemical or biological composition to bevacizumab or erlotinib hydrochloride * No abnormalities of the cornea, including any of the following: History of dry eye syndrome or Sjögren's syndrome; Congenital abnormality (e.g., Fuch's dystrophy); Abnormal slit-lamp examination using a vital dye (e.g., fluorescein, Bengal-Rose); Abnormal corneal sensitivity test (e.g., Schirmer test or similar tear production test) * No stroke or transient ischemic attack within the past 6 months * No uncontrolled high blood pressure, history of labile hypertension, or history of poor compliance with an antihypertensive regimen * No unstable angina pectoris within the past 6 months * No symptomatic congestive heart failure * No myocardial infarction within the past 6 months * No serious uncontrolled cardiac arrhythmias * No uncontrolled diabetes mellitus * No active or uncontrolled infection * No impaired GI function or disease that may significantly alter the absorption of erlotinib hydrochloride (e.g., ulcerative disease, uncontrolled nausea, vomiting, or diarrhea, malabsorption syndrome, or bowel obstruction) * Able to swallow tablets * No psychiatric illness or social situation that would limit compliance with study requirements * No history of nephrotic-range protein * No history of bleeding diathesis * No encephalopathy * No serious nonhealing wounds, skin ulcers, or bone fractures * No clinically significant peripheral vascular disease * No known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies * No history of a GI bleed that required procedural intervention (e.g., variceal banding, surgical shunt, transvenous intrahepatic porto-systemic shunt \[TIPS\]) within the past 3 months * No significant traumatic injury within the past 28 days * No other prior malignancy within the past 5 years except for the following: Adequately treated basal cell or squamous cell skin cancer; Adequately treated in situ cervical cancer; Stage I or II cancer from which the patient is currently in complete remission; Stage I chronic lymphocytic leukemia * Recovered from all therapy-related toxicities * No more than 1 prior systemic or liver directed drug therapy including transarterial chemoembolization (TACE) (multiple TACEs will count as 1 prior regimen irrespective of their total numbers) that were used for HCC * No chemotherapy for HCC within the past 4 weeks (6 weeks for nitrosoureas or mitomycin C) * No biological therapy or immunotherapy for HCC within the past 4 weeks * Prior surgery, regional therapy (e.g., transarterial embolization), liver transplantation, or other liver-directed ablative therapies of discrete lesions allowed provided any related progressive or recurrent disease is documented * No cryotherapy, radiofrequency ablation, ethanol injection, or photodynamic therapy within the past 6 weeks: Indicator lesions must be outside the area of prior treatment OR if the lesion is inside the area of prior treatment, there must be clear evidence of disease progression associated with that lesion * No core biopsy within the past 7 days * No radiotherapy within the past 4 weeks * No prior antiangiogenesis agent or antiepidermal growth factor receptor drug * No prior treatment with hepatic arterial infusion with chemotherapy or yttrium Y 90-labeled microspheres * No other concurrent investigational agents * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent anticancer therapy * Concurrent full-dose anticoagulants (e.g., warfarin) with international normalized ratio (INR) \> 1.2 allowed provided the following criteria are met: An in-range INR (usually between 2 and 3) on a stable dose of oral anticoagulant (or on a stable dose of low molecular weight heparin) * AND (continued from above) No active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels, gastrointestinal \[GI\] ulceration, or known varices) * No concurrent major surgical procedures * Histologically confirmed hepatocellular carcinoma (HCC): * No fibrolamellar subtype HCC * Advanced disease * Not a candidate for surgical resection or liver transplantation * Measurable disease: * Edges of the indicator lesion must be clearly distinct on CT scan * Lesions that measure at least 1 cm but less than 2 cm only must use spiral CT imaging for both pre- and post-treatment tumor assessments * Child's Pugh classification A or B * No primary brain tumor, brain metastasis, or other central nervous system (CNS) diseases * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Platelet count \>= 75,000/mm\^3 * No major surgery (e.g., laparotomy), open biopsy, or minor surgery (e.g., insertion of a vascular access device) within the past 4 weeks * No interstitial pneumonia or extensive and symptomatic interstitial fibrosis of the lung * No abdominal fistula, GI perforation, or intra-abdominal abscess within the past 28 days * No concurrent prophylactic hematopoietic colony-stimulating factors