Evaluating SINE KPT-330 in Treating Patients With Melanoma That Cannot Be Removed By Surgery

Inclusion Criteria: * Written informed consent in accordance with federal, local, and institutional guidelines * Patients with unresectable melanoma * Patients must have received a biologic therapy (e.g. interleukin 2) and a BRAF and/or MEK inhibitor (if tumor contains the V600E or V600K mutation) for 628 metastatic disease. If patient did not receive such agents, rationale for not treating the patients with the 629 agent must be cleared with the study PI (ie no V600e/k BRAF mutation or patient with autoimmunity, thus 630 not eligible for biologic therapy). * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Total white blood cell (WBC) count \>= 3000/mm\^3 * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Bilirubin \< 2 times the upper limit of normal (ULN) (except patients with Gilbert's syndrome who must have a total bilirubin of \< 3 times ULN) * Alanine aminotransferase (ALT) \< 2.5 times ULN; in the case of known (radiological and/or biopsy documented) liver metastasis, ALT \< 5.0 times ULN is acceptable * Estimated creatinine clearance of \>= 50 mL/min, calculated using the formula of Cockroft and Gault * Female patients of child-bearing potential must agree to use dual methods of contraception and have a negative serum pregnancy test at screening, and male patients must use an effective barrier method of contraception if sexually active with a female of child-bearing potential; acceptable methods of contraception are condoms with contraceptive foam, oral, implantable or injectable contraceptives, contraceptive patch, intrauterine device, diaphragm with spermicidal gel, or a sexual partner who is surgically sterilized or post-menopausal; for both male and female patients, effective methods of contraception must be used throughout the study and for three months following the last dose Exclusion Criteria: * Patients who are pregnant or lactating * Radiation, chemotherapy, immunotherapy or any other systemic anticancer therapy =\< 2 weeks prior to initiation of therapy * Major surgery within four weeks before initiation of therapy * Unstable cardiovascular function: * Symptomatic ischemia, or * Uncontrolled clinically significant conduction abnormalities (e.g.: ventricular tachycardia on antiarrhythmics are excluded and 1st degree atrioventricular (AV) block or asymptomatic left anterior fascicular block \[LAFB\]/right bundle branch block \[RBBB\] will not be excluded) * Congestive heart failure (CHF) of New York Heart Association (NYHA) class \>= 3, or * Myocardial infarction (MI) within 3 months of initiation of therapy * Uncontrolled active infection within one week prior to first dose * Known to be human immunodeficiency virus (HIV) seropositive * Known active hepatitis A, B, or C infection; or known to be positive for hepatitis C virus (HCV) ribonucleic acid (RNA) or HBsAg (hepatitis B virus \[HBV\] surface antigen) * Patients with active central nervous system (CNS) malignancy * Asymptomatic small lesions are not considered active * Treated lesions may be considered inactive if the patient is able to taper off steriods without any recurrent neurologic symptoms. * Patients will be excluded if they have had a major resection of the bowel that could influence absorption, inflammatory bowel disease, or other gastrointestinal conditions with increased risk of perforation, history of abdominal fistula, gastrointestinal perforation within 28 days prior to beginning study treatment * Grade \>= 2 peripheral neuropathy within 14 days prior to initiation of therapy * History of seizures, movement disorders or cerebrovascular accident within the past 5 years * Patients with known macular degeneration or uncontrolled glaucoma * In the opinion of the investigator, patients who are significantly below their ideal body weight * Serious psychiatric or medical conditions that could interfere with treatment * Participation in an investigational anti-cancer study within 3 weeks prior to initiation of therapy * Concurrent therapy with approved or investigational anticancer therapeutic