Propranolol Hydrochloride in Treating Patients With Locally Recurrent or Metastatic Solid Tumors That Cannot Be Removed By Surgery

Inclusion Criteria: * Patients must have histologically-proven locally-recurrent or metastatic solid tumor; the first 10 patients may have cancer of any histology; preference will be given to patients with metastatic ovarian cancer, breast cancer, and malignant melanoma, as these malignancies have been shown to be sensitive to manipulation of the beta-adrenergic receptor; the final twenty-five patients to be accrued must have locally-recurrent or metastatic malignant melanoma that is not surgically resectable. An additional cohort of 10 patients with BCLC stages A to C locally advanced or metastatic hepatocellular carcinoma (HCC) that is not surgically resectable will also be enrolled (See appendix for BCLC staging system). Patients with liver transplantation will not be eligible. * The diagnosis of hepatocellular carcinoma may be made by one of the following methods: 1. Pathologically (histologically or cytologically) proven diagnosis of HCC. 2. At least one solid liver lesion or vascular tumor thrombosis (involving portal vein, IVC and/or hepatic vein) \> 1 cm with arterial enhancement and delayed washout on multiphasic computerized tomography (CT) or magnetic resonance imaging (MRI) in the setting of cirrhosis or chronic hepatitis B or C without cirrhosis. 3. For patients whose CURRENT disease is vascular only: Enhancing vascular thrombosis (involving portal vein, IVC and/or hepatic vein) demonstrating early arterial enhancement and delayed washout on multi-phasic CT or MRI, in a patient with known HCC (diagnosed according to criteria in (a) or (b). * Patients may have had any number of prior systemic therapies; patients need not have exhausted standard therapy for their disease, but must be stable and must not have actively progressing * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Karnofsky \>= 60% * Life expectancy of greater than 6 months * Patients (except for the HCC cohort) must have normal organ and marrow function as defined below: * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal * Creatinine within normal institutional limits OR * Creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Parameters for the HCC cohort: * leukocytes \> or = 3000/mcl * absolute neutrophil count \> or =1000/mcl * platelets \> or = 70,000 * total bilirubin \< or = 2mg/dL * AST/ALT \<6 times ULN * creatinine within normal institutional limits OR * creatinine clearance \> or = 60mL/min/1.73m2 for patients with creatinine levels above institutional normal level * INR \< or = 1.7 * The effects of propranolol on the developing human fetus may be detrimental. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * Patients with brain metastases may participate in this clinical study provided that symptoms have been controlled with standard therapies and/or appropriate medications; the principal investigator (P.I.) will carefully evaluate the suitability of patient participation when brain metastases are present Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients may not be receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to propranolol * Uncontrolled hypertension * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Patients with significant lung disease, an ejection fraction less than 40%, or a resting heart rate less than 60/min will not be enrolled * Pregnant women are excluded from this study because propranolol is an agent with the potential for teratogenic or abortifacient effects * Patients who are currently receiving a beta-blocker for another medical condition will be excluded from this study; patients with extremes of blood pressure (e.g., systolic blood pressure \[SBP\] \> 150 or \< 100) may be excluded from participation if the treating physician feels that this medical condition has not been adequately addressed by the patient's primary care physician * Patients with worsening depression that has not been addressed clinically will be excluded from this study