BElumosudil for Bronchiolitis Obliterans Prevention/Therapy (BEBOP)

Inclusion Criteria Cohort A: * Diagnosis of BOS after HCT using pulmonary function testing, per the NIH diagnostic criteria17 OR the Atypical BOS criteria33 3.1.2.1 NIH Diagnostic Criteria for BOS. All of the following must be met: * FEV1/VC \< 0.7 or \<5th percentile of predicted (FEV1 = Forced Expiratory Volume in 1 second; VC = Vital Capacity (either FVC, Forced Vital Capacity, or SVC, Slow Vital Capacity, whichever is greater) * FEV1 \<75% of predicted with ≥ 10% absolute decline over less than 2 years. FEV1 should not correct to \>75% of predicted with albuterol, and the absolute decline for the corrected values should still remain ≥ 10% over 2 years. * Absence of active infection in the respiratory tract, documented with investigations directed by clinical symptoms, such as chest radiographs or computed tomographic scans or microbiologic cultures (sinus aspiration, upper respiratory tract viral screen, sputum culture, bronchoalveolar lavage). * One of the two supporting features of BOS: * i - Evidence of air trapping by expiratory CT or small airway thickening or bronchiectasis by high-resolution chest CT OR * ii - Evidence of air trapping by PFTs: RV (Residual Volume) \> 120% of predicted or RV/TLC elevated outside the 90% confidence interval (RV/Total Lung Capacity). * Atypical Criteria for BOS: * FEV1 \<80% of predicted with ≥ 10% absolute decline over the last 2 years or since transplant. The remote comparator can be an evaluation of PFTs done within 2 years of the PFTs assessment being evaluated to determine eligibility or the PFT assessment done prior to transplant. * VC \< 80% of predicted. * FEV1/VC \> 0.7. * Absence of active infection in the respiratory tract, documented with investigations directed by clinical symptoms, such as chest radiographs or computed tomographic scans or microbiologic cultures (sinus aspiration, upper respiratory tract viral screen, sputum culture, bronchoalveolar lavage) or active non-infectious lung disease (such as interstitial lung disease) that explain spirometric changes or chest CT findings. Inclusion Criteria for Cohort B: -Diagnosis of BOS-0p * Decline in FEV1 of 10% - 19% of predicted compared with pretransplant testing OR * Decline in predicted FEF25-75% (Forced Expiratory Flow between 25% and 75% of vital capacity) \> 25% Inclusion Criteria for Cohorts A and B: * Age ≥18 years. Belumosudil is currently being tested in pediatric populations and the safety and efficacy in pediatric patients have not yet been established. A protocol amendment to include pediatric patients will be considered once safety in pediatric patients is established. * ECOG performance status ≤2 (Karnofsky ≥ 60%). * Participants must have adequate organ and marrow function as defined below: * WBC ≥ 3,000/μL * Absolute neutrophil count ≥ 1,500/ μL * Platelets ≥ 50,000/mcL * AST(SGOT)/ALT(SGPT) ≤ 5 × institutional ULN * No evidence of relapsed malignancy at the time of enrollment. Formal re-staging is not required for trial entry. * All females of childbearing potential must have a negative serum or urine pregnancy test \< 7 days before study drug administration. * The ability to understand and willingness to sign a written consent document. Exclusion Criteria for Cohorts A and B: * Participants who have received prior therapy specifically for BOS. Therapy for cGVHD in the absence of BOS is permissible. * Prior exposure to belumosudil. * Participants who are receiving any other investigational immunosuppressive agents for cGVHD. * Presence of an active uncontrolled infection. An active uncontrolled infection is defined as hemodynamic instability attributable to sepsis or new symptoms, worsening physical signs, or radiographic findings attributable to infection. Persistent fever without signs or symptoms will not be interpreted as an active uncontrolled infection. * Known human immunodeficiency virus infection. Interactions between belumosudil and anti-retroviral agents have not been established. * Active hepatitis B virus (HBV) or hepatitis C virus infection that requires treatment or at risk for HBV reactivation. At risk for HBV reactivation is defined as hepatitis B surface antigen positive or anti-hepatitis B core antibody positive. Subjects with previous positive serology results must have negative polymerase chain reaction results. Subjects whose immune status is unknown or uncertain must have results confirming immune status before enrollment.