Low-Dose Total Lymphoid Irradiation in Treating Patients With Refractory Chronic Graft-versus-Host Disease After Donor Stem Cell Transplant

Inclusion Criteria: * Patients may have received a prior allogeneic hematopoietic stem cell transplant (alloHSCT) for any indication and from any donor * Patients must have a diagnosis of cGvHD, in accordance with National Institutes of Health (NIH) guidelines; patients with "overlap syndrome" are also eligible; NOTE: Patients with recurrent, late onset and/or persistent acute GvHD (alone) are not eligible * Patients with chronic GvHD who have been exposed to two or more lines of therapy, including at least one of which was composed of a glucocorticoid and a calcineurin inhibitor are eligible. * Patients must have active, but not rapidly progressive, refractory cGvHD; any degree of severity (as per NIH criteria) and/or pattern of organ involvement may be considered; that said, patients with more severe and/or extensive chronic GvHD are expected to be the usual candidates for therapy * As above, GvHD should be controlled to a degree that would potentially allow no additional requirement for systemic IST before and following TLI =\< -15 and \>= day (d) +45, respectively * The ability to administer protocol doses of TLI (i.e., 100, 200 or 300 cGy) without exceeding cumulative doses of radiation must be established; for patients with prior radiotherapy exposure, this determination will be made by Dr. Greven (or her designee) using published guidelines for excessive organ exposure * Karnofsky performance status (KPS) \>= 60% * White blood cells \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Hemoglobin \>= 10.0 g/dL * Platelets \>= 100,000/mcL * NOTE: If such hematologic abnormalities are present and deemed due to the process of cGvHD, such requirements may be waived with the approval of the PI * Patients must have non-hematologic organ function as defined below: * Left ventricular ejection fraction (LVEF) \> 40% * Key pulmonary function tests (PFTs) \> 40% * No further criteria for non-hematologic organ function are specified; however, if moderate-to-severe (major) organ function is present, such should be discussed with the PI, as various degrees of non-hematologic organ dysfunction may compromise either (or both) outcomes and toxicity evaluation * If there is concern regarding potential reversibility of any specific organ dysfunction, this issue should be addressed by consultation with an appropriate sub-specialist * Ability to understand and the willingness to sign an institutional review board (IRB)-approved informed consent document Exclusion Criteria: * Patients with evidence of persistent or active malignancy or uncontrolled infection at the time of study entry * Patients who are pregnant or breastfeeding