Selinexor, Carfilzomib, and Dexamethasone in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria:

* Written informed consent in accordance with federal, local, and institutional guidelines
* Aged 18 years or older
* Eastern Cooperative Oncology Group (ECOG) performance status of 0-2
* Diagnosis of multiple myeloma as per International Myeloma Working Group (IMWG) uniform criteria
* Measurable disease by IMWG as defined by at least one of the following:

  * Serum M-protein \>= 0.5 g/dL
  * Urine M-protein \>= 200 mg in a 24-hour collection
  * Serum free light chain level \>= 10 mg/dL provided the free light chain ratio is abnormal
  * Measurable plasmacytoma; if plasmacytoma measurement is the only measurable disease, subject eligibility must be reviewed with lead principal investigator (PI) prior to signing consent
* Relapsed/refractory multiple myeloma with progressive disease at study entry
* Subjects must have been treated with at least 2 prior therapies including a proteasome inhibitor and a cereblon-binding agent

  * Subjects who are refractory to carfilzomib may enroll throughout the trial; carfilzomib refractory status is defined by IMWG criteria: disease that is nonresponsive while on salvage therapy, or progresses within 60 days of last therapy in patients who have achieved minimal response (MR) or better at some point previously before then progressing in their disease course
* Ability to adhere with the study visit schedule and other protocol procedures
* Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L; screening ANC should be independent of growth factor support for over one week for all patients
* Hemoglobin \>= 8 g/dL; subjects may receive red blood cell transfusions as clinically indicated per institutional guidelines but screening hemoglobin should be independent of red blood cell transfusion for at least 3 days prior to cycle 1 day 1
* Platelet count \>= 50,000mm\^3; platelet count should be independent of transfusions for at least 14 days for eligibility
* Total 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 =\< 2.5 times ULN is acceptable
* Estimated creatinine clearance of \>= 30 mL/min, calculated using the formula of Cockroft and Gault
* Female patients of child-bearing potential must agree practice abstinence or use dual methods of contraception during treatment and for 90 days after last dose of study drug.
* Female patients of child-bearing potential must have negative pregnancy test at screening
* Male patients must agree practice abstinence or use effective barrier methods of contraception during treatment and for 90 days after last dose of study drug
* Male patients must agree not to donate semen or sperm treatment and for 90 days after last dose of carfilzomib

Exclusion Criteria:

* Patients who are pregnant or lactating
* Radiation, chemotherapy, or immunotherapy or any other anticancer therapy =\< 2 weeks prior to cycle 1 day 1
* Concurrent therapy with approved or investigational anticancer therapeutic other than steroids
* Major surgery within four weeks before cycle 1 day 1
* Unstable angina or myocardial infarction within 4 months prior to randomization, New York Heart Association (NYHA) class III or IV heart failure, left ventricular ejection fraction (LVEF) \< 40%, uncontrolled angina, history of severe coronary artery disease, severe uncontrolled ventricular arrhythmias including uncontrolled chronic atrial fibrillation/atrial flutter, history of torsades de pointe, sick sinus syndrome, or electrocardiographic evidence of acute ischemia or grade 3 conduction system abnormalities unless subject has a pacemaker
* Subject has plasma cell leukemia or Waldenstrom's macroglobuleinemia or POEMS syndrome (polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes) or amyloidosis
* Uncontrolled hypertension or uncontrolled diabetes within 14 days prior to randomization
* Uncontrolled infection requiring parenteral antibiotics, antivirals, or antifungals within 14 days prior to first dose; patients with controlled infection or on prophylactic antibiotics are permitted in the study
* 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)
* Non-hematologic malignancy within the past 3 years with the exception of a) adequately treated basal cell carcinoma, squamous cell skin cancer, or thyroid cancer; b) carcinoma in situ of the cervix or breast; c) prostate cancer of Gleason grade 6 or less with stable prostate-specific antigen levels; or d) cancer considered cured by surgical resection or unlikely to impact survival during the duration of the study, such as localized transitional cell carcinoma of the bladder or benign tumors of the adrenal or pancreas
* Patients with markedly decreased visual acuity in the opinion of the treating investigator after completion of screening ophthalmologic exam
* Significant neuropathy (grades 3-4, or grade 2 with pain) within 14 days prior to randomization
* Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib)
* Any underlying condition that would significantly interfere with the absorption of an oral medication
* Serious psychiatric or medical conditions that could interfere with treatment
* Contraindication to any of the required concomitant drugs or supportive treatments, including hypersensitivity to all anticoagulation and antiplatelet options, antiviral drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment
* Subjects with pleural effusions requiring thoracentesis or ascites requiring paracentesis within 14 days prior to randomization
* Patients with coagulation problems and active bleeding in the last month prior to cycle 1 day 1 (peptic ulcer, epistaxis, spontaneous bleeding)
* Previous Selinexor exposure