Vismodegib in Treating Patients With Steroid-Refractory Chronic Graft-Versus-Host Disease

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 12 months * Leukocytes \>= 3,000/microliter (mcL) * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 50,000/mcL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase (SGOT))/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase (SGPT)) =\< 2.5 x institutional upper limit of normal * Creatinine =\< 1.5 mg/dl OR creatinine clearance \>= 55 mL/min using the Cockcroft-Gault equation for patients with creatinine levels above 1.5 mg/dl * Patients with chronic GVHD diagnosed within 3 years after hematopoietic stem cell transplant (HSCT) for any disease, with any graft, and any conditioning regimen with at least one manifestation secondary to fibrosis, including: sclerodermatous skin changes, dry mouth, dry eye, esophageal strictures, or vaginal GVHD * Failure to respond to corticosteroids, defined as: * Progression of chronic GVHD despite optimal first line therapy (\> 0.5 mg/kg/day of prednisone dose equivalent (PDE) for two weeks) or * No improvement after 4-8 weeks of sustained therapy; sustained therapy should include 2 weeks of \> 0.5 mg/kg/day of PDE or * Inability to taper steroid dosage to less than 0.5 mg/kg/day of PDE without worsening of chronic GVHD or * Need for second or third line therapy beyond corticosteroids and calcineurin inhibitors or sirolimus, irrespective of other criteria * 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 study entry, for the duration of study participation, and for at least 24 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 milli-international unit (mIU)/mL) within 7 days 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's understanding of GDC-0449 cause serious or life-threatening birth defects; patients must continue highly effective contraception during therapy and for 24 months after the last dose of GDC-0449 * 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 12 months in a woman \> 45 years old * Male patients should use condoms with spermicide, even after a vasectomy, during sexual intercourse with female partners while being treated with GDC-0449 and for 3 months after the last dose to avoid exposing an embryo or fetus to GDC-0449 * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are eligible provided that they meet the following criteria in addition to the other protocol criteria: * Cancer as the only acquired immunodeficiency syndrome (AIDS)-defining condition * Cluster of differentiation (CD)4 cell count \>= 250 * Treatment sensitive HIV and prospects for long term survival on the basis of HIV disease alone * Willing to take anti-HIV therapy that will have minimal potential for pharmacokinetic interactions with GDC-0449 Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients who are receiving any other investigational agents * Patients with known brain metastases should be excluded from this clinical trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition to GDC-0449 * Patients receiving any medications or substances that are strong inducers/inhibitors or substrates of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4)/5, cytochrome P450, family 2, subfamily C, polypeptide 9 (CYP2C9), CYP2C8, or CYP2C19 are ineligible; as part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product * Patients with malabsorption syndrome or other condition that would interfere with intestinal absorption; patients must be able to swallow capsules * Patients with clinically important history of liver disease, including viral or other hepatitis or cirrhosis are ineligible * Patients with uncontrolled hypocalcemia, hypomagnesemia, hyponatremia or hypokalemia defined as less than the lower limit of normal for the institution, despite adequate electrolyte supplementation are excluded from this study * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with GDC-0449 * More than 2 lines of therapy beyond corticosteroids with or without calcineurin inhibitors or sirolimus * Relapsed malignancy after transplantation