Sorafenib in Treating Patients With Relapsed or Refractory Multiple Myeloma

Inclusion Criteria:

* Patients must have a confirmed diagnosis of previously treated, active multiple myeloma, with measurable disease present to evaluate response; all tests for establishing baseline disease status (serum protein electrophoresis, urine protein electrophoresis and bone marrow biopsy) must be performed within 28 days prior to registration and MUST be documented on the Baseline and Follow-up Tumor Assessment Form for Multiple Myeloma
* Patients must have relapsed or resistant disease, defined as relapsing after autologous stem cell transplantation or is either relapsing or is resistant after \>= 1 line of prior therapy for myeloma; a minimum of 42 days must have elapsed since prior transplant

  * Relapse: is defined as the occurrence of any of the following during or after previous treatment:

    * A myeloma protein increase by more than 100% from the lowest previously recorded level
    * A myeloma protein increase above the response criteria for PR
    * Reappearance of any myeloma peak that had disappeared during the previous treatment
    * Increase in the size and number of lytic bone lesions and/or focal lesions recognized in radiographic studies (x-ray, MRI, PET and/or CT scans)
  * Resistant disease: is defined as disease not responding (i.e. not achieving CR, R, PR) to previous therapy
* Patients must be off myelosuppressive chemotherapy for \>= 21 days (\>= 6 weeks for nitrosoureas) and non-myelosuppressive chemotherapy and XRT for \>= 14 days and recovered from all treatment associated toxicities prior to registration
* Patients must have a Zubrod Performance Status (PS) of 0-2
* Patients must have received no prior treatment with BAY 43-9006
* Patients must have currently have no significant neurotoxicity, defined as Grade \>= 2 neurotoxicity per NCI Common Terminology Criteria for Adverse Events (CTCAE) Version 3.0
* Patients must have no evidence of POEMS (polyneuropathy, organomegaly, endocrinopathy, presence of M-protein, and skin changes) Syndrome
* There must be no active infection requiring antibiotics
* Bilirubin =\< 1.5 times the institutional upper limit of normal (IULN)
* AST (SGOT or SGPT) =\< 5 times the institutional upper limit of normal (IULN)
* Serum creatinine =\< the institutional upper limit of normal (IULN)
* ANC \> 750/ul
* Platelet count \> 75,000/ul
* Patients must be able to take oral medication without crushing, dissolving or chewing tablets
* Patients must not be taking the cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine, and phenobarbital), rifampin, or St. John's Wort
* Patients must not have a significant history of cardiac disease, e.g., uncontrolled hypertension, unstable angina, congestive-heart failure, and myocardial infarction within the last six months, or cardiac ventricular arrhythmias requiring medication
* Patients must not have any evidence of bleeding diathesis, uncontrolled diabetes mellitus, or other serious or psychiatric illness that could potentially interfere with the completion of treatment according to this protocol
* Patients must not be on therapeutic anticoagulation
* No prior malignancy is allowed except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer for which the patient has been disease free for at least three years
* Pregnant or nursing women may not participate in this trial because of increased risk of fetal harm including fetal death from the chemotherapeutic agents; women/men of reproductive potential may not participate unless they have agreed to use an effective contraceptive method
* Institutions must have IRB approval of S0309 ("Myeloma Specimen Repository Protocol, Ancillary"); patients must be offered participation in S0309; with the patient's consent, bone marrow aspirates and serum specimens will be submitted for testing via S0309; patients must be registered separately to S0309 in order for institutions to receive credit for specimen submission to S0309; NOTE: immediately following S0434 registration, the CRA will need to have completed the S0309 Registration Form and eligibility worksheet in hand for use
* All patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines
* At the time of patient registration, the treating institution's name and ID number must be provided to the Data Operations Center in Seattle in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered into the data base