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 tre…