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 t…