Vismodegib After Stem Cell Transplant in Treating Patients With High-Risk First Remission or Relapsed Multiple Myeloma

Inclusion Criteria:

* Patients must have histologically or cytologically confirmed multiple myeloma meeting criteria with symptomatic disease requiring treatment; patients considered to have high risk disease (defined as chromosome 13 deletion by cytogenetics; t(4;14), t(14;16) or 17p deletion by fluorescence in situ hybridization \[FISH\], B2-M \> 5.5 g/dL, immunoglobulin A \[IgA\] phenotype) in first remission (\>= partial remission \[PR\]) or patients with relapsed myeloma responding to salvage therapy (\>= PR) based on the International Uniform Response Criteria are eligible
* Patients must have measurable disease utilizing serum or urine protein electrophoresis or serum kappa / lambda light chain assay
* Patients must be planning to proceed to single autologous transplantation according to institutional standards and must receive this transplantation prior to implementation of GDC-0449
* Concomitant bisphosphonate use is allowed as clinically indicated
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Life expectancy of greater than 6 months
* Women of child-bearing potential and men must use two forms of contraception (i.e., barrier contraception and one other method of contraception) at least 4 weeks prior to GDC-0449 treatment, for the duration of study participation, and for at least 12 months post-treatment; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately

  * Women of childbearing potential are required to have a negative serum pregnancy test (with a sensitivity of at least 25 mIU/mL) within 10-14 days and within 24 hours prior to the first dose of GDC-0449 (serum or urine); a pregnancy test (serum or urine) will be administered every 4 weeks if their menstrual cycles are regular or every 2 weeks if their cycles are irregular while on study within the 24-hour period prior to the administration of GDC-0449; a positive urine test must be confirmed by a serum pregnancy test; prior to dispensing GDC-0449, the investigator must confirm and document the patient's use of two contraceptive methods, dates of negative pregnancy test, and confirm the patient understands of GDC-0449 cause serious or life-threatening birth defects
  * Women of childbearing potential are defined as follows:

    * Patients with regular menses
    * Patients with amenorrhea, irregular cycles, or using a contraceptive method that precludes withdrawal bleeding
    * Women who have had a tubal ligation
  * Women are considered not to be of childbearing potential for the following reasons:

    * The patient has undergone hysterectomy and/or bilateral oophorectomy
    * The patient is post-menopausal defined by amenorrhea for at least 1 year in a women
* Human immunodeficiency virus (HIV)-positive patients without a prior acquired immune deficiency syndrome (AIDS)-defining illness and a CD4 count 400/millimeter\^3 and either do not require anti-HIV therapy or are taking anti-HIV therapy that would not interfere with GDC-0449 (e.g. not taking zidovudine, protease inhibitors or non-nucleoside reverse transcriptase inhibitors) are eligible
* Ability to understand and the willingness to sign a written informed consent document