Riluzole and Sorafenib Tosylate in Treating Patients With Advanced Solid Tumors or Melanoma

Inclusion Criteria: * Patients must have histologically proven solid tumors (Phase I) with biopsiable tumor (expansion cohort) refractory to standard therapy or for whom no standard therapy exists or who decline standard therapy * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Patients must be willing and able to sign informed consent * Unlimited prior therapies are permitted for patients enrolled in the dose escalation phase of the study; patients in the expansion cohort of the study may not have any prior therapy with riluzole or sorafenib and must have biopsiable tumor * Patients may have measurable or evaluable disease * Absolute neutrophil count (ANC) \>= 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN * International normalized ratio (INR) =\< 1.5 x institutional ULN * Creatinine =\< 2 x ULN * Patients with brain lesions that have been treated with whole brain radiotherapy and are clinically stable for at least 4 weeks, are not taking steroids and are not receiving enzyme-inducing anticonvulsants will be eligible Exclusion Criteria: * Serious concomitant systemic disorders (including active infections) that would compromise the safety of the patient or compromise the patient's ability to complete the study, at the discretion of the investigator * For patients who have received gamma knife or stereotactic radiosurgery, a 2 week washout is required; patients who have had other types of radiotherapy, chemotherapy or biologic agents within 3 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 3 weeks earlier to =\< grade 1; at least 4 weeks must have elapsed since any major surgery; patients with prostate cancer may continue to receive hormonal therapy * History of allergic reactions attributed to riluzole or sorafenib * Women of child-bearing potential and men must agree to use adequate contraception (hormonal, barrier method of birth control, abstinence) prior to study entry, for the duration of study participation, and for 2 weeks after discontinuation of riluzole and/or sorafenib; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately; pregnant (positive pregnancy test) or lactating patients cannot participate * Known human immunodeficiency virus (HIV) infection or known history of active hepatitis B or C infection * Current, recent (within 4 weeks of the first treatment of this study), or planned participation in an experimental drug study (prevention trials are permitted if the trial is not testing a novel experimental agent) * Cardiac disease: congestive heart failure \> class II New York Heart Association (NYHA); patients must not have unstable angina (anginal symptoms at rest) or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months * History of stroke within six months * Clinically significant peripheral vascular disease * Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy * Uncontrolled hypertension, defined as systolic blood pressure \> 150 mm Hg or diastolic blood pressure \> 90 mm Hg, despite optimal medical management * Active clinically serious infection \> Common Terminology Criteria for Adverse Events (CTCAE) grade 2 * Any of the following within 6 months prior to first dose of treatment: myocardial infarction, symptomatic coronary artery disease (severe or unstable angina), artery bypass graft, uncontrolled arrhythmias, symptomatic congestive heart failure, cerebrovascular accident or transient ischemic attack, or pulmonary embolus * Pulmonary hemorrhage/bleeding event \>= CTCAE grade 2 within 4 weeks of first-dose of study drug * Any other hemorrhage/bleeding event \>= CTCAE grade 3 within 4 weeks of first dose of study drug * Evidence or history of bleeding diathesis or coagulopathy * Major surgery or significant traumatic injury within 4 weeks of first study drug * The eligibility of patients taking medications that are potent modulators of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4), cytochrome P450, family 2, subfamily B, polypeptide 6 (CYP2B6), subfamily 2, polypeptide 8 (2C8) will be determined following a review of their case by the principal investigator; every effort should be made to switch patients taking such agents or substances to other medications * Any condition that impairs the patient's ability to swallow whole pills * Any malabsorption problem * Anticipation of need for major surgical procedure during the course of the study * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 6 months prior to day 1 of treatment * Serious, non-healing wound, ulcer, or bone fracture * Inability to comply with study and/or follow-up procedures * Anticoagulation with Lovenox (enoxaparin) is permitted, however, patients on anticoagulation with warfarin are not permitted on this study