Biomarker-Guided Feasibility/Efficacy Trial of Ruxolitinib in Patients With High-Risk of Chronic Graft-Versus-Host Disease Development After Allogeneic Hematopoietic Cell Transplantation

Inclusion Criteria: * PRE-SCREENING: Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * PRE-SCREENING: Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study principal investigator (PI) approval * PRE-SCREENING: Age: ≥ 18 years * PRE-SCREENING: Karnofsky performance status ≥ 80 * PRE-SCREENING: Patients must have undergone allogeneic hematopoietic cell transplantation with peripheral blood stem cells as graft source. Note: Patients receiving manipulated graft are not included * PRE-SCREENING: Morphologic remission per day +30 bone marrow * PRE-SCREENING: Any conditioning regimen (myeloablative, reduce intensity/non-myeloablative conditioning) is allowed * PRE-SCREENING: Any GVHD prophylaxis (tacrolimus-sirolimus, tacrolimus-methotrexate, or post-transplant cyclophosphamide) is allowed * PRE-SCREENING: Life expectancy of more than 6 months * PRE-SCREENING: Absolute neutrophil count (ANC) \> 1000/mm\^3 (to be performed between day +70 and +100 after HCT unless otherwise stated) * PRE-SCREENING: Hemoglobin ≥ 8.0 gm/dL (to be performed between day +70 and +100 after HCT unless otherwise stated) * PRE-SCREENING: Platelets ≥ 50,000/mm\^3 (to be performed between day +70 and +100 after HCT unless otherwise stated) * Note: Patients with lower counts can enroll if infection cytomegalovirus (CMV)/human herpesvirus 6 (HHV6), etc. is being treated actively * PRE-SCREENING: Total bilirubin ≤ 1.5 X upper limit of normal (ULN) (unless has Gilbert's disease) (to be performed between day +70 and +100 after HCT unless otherwise stated) * PRE-SCREENING: Aspartate aminotransferase (AST) =\< 3.0 x ULN (to be performed between day +70 and +100 after HCT unless otherwise stated) * PRE-SCREENING: Alanine aminotransferase (ALT) =\< 3.0 x ULN (to be performed between day +70 and +100 after HCT unless otherwise stated) * PRE-SCREENING: Glomerular filtration rate (GFR) ≥ 50 ml/min (to be performed between day +70 and +100 after HCT unless otherwise stated) * PRE-SCREENING: Women of childbearing potential (WOCBP): negative urine or serum pregnancy test (to be performed between day +70 and +100 after HCT unless otherwise stated) * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * PRE-SCREENING: Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 3 months after the last dose of protocol therapy * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) * AFTER DAY +100 TEST RESULTS PATIENTS WITH MODERATE TO HIGH-RISK cGVHD (TREATMENT ARM): Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * AFTER DAY +100 TEST RESULTS PATIENTS WITH MODERATE TO HIGH-RISK cGVHD (TREATMENT ARM): Elevated serum/plasma levels of ST2, CXCL9, MMP-3, and OPN as indicated by moderate or severe risk of chronic GVHD in the test results * AFTER DAY +100 TEST RESULTS PATIENTS WITH MODERATE TO HIGH-RISK cGVHD (TREATMENT ARM): No use of ruxolitinib or other Jak inhibitors in the past 14 days * AFTER DAY +100 TEST RESULTS PATIENTS WITH MODERATE TO HIGH-RISK cGVHD (TREATMENT ARM): Morphologic remission per day +100 bone marrow * AFTER DAY +100 TEST RESULTS PATIENTS WITH MODERATE TO HIGH-RISK cGVHD (TREATMENT ARM): Adequate hematopoietic recovery (hemoglobin \[Hgb\] ≥ 8 g/dL, platelets \[PLT\] ≥ 50K/ mm\^3) * AFTER DAY +100 TEST RESULTS PATIENTS WITH MODERATE TO HIGH-RISK cGVHD (TREATMENT ARM): Negative serum or urine pregnancy test (female participants with childbearing potential only) * AFTER DAY +100 TEST RESULTS PATIENTS WITH MODERATE TO HIGH-RISK cGVHD (TREATMENT ARM): Absence of active infection not responding to antibiotics * AFTER DAY +100 TEST RESULTS PATIENTS WITH MODERATE TO HIGH-RISK cGVHD (TREATMENT ARM): Absence of progressive acute GVHD. Note: prednisone administration (flat dose of \< 0.25 mg/kg) is allowed. Patients receiving any other medication to control active/progressive GVHD will be excluded * AFTER DAY +100 TEST RESULTS PATIENTS WITH MODERATE TO HIGH-RISK cGVHD (TREATMENT ARM): Absence of any clinically significant uncontrolled sickness * AFTER DAY +100 TEST RESULTS PATIENTS WITH LOW-RISK cGVHD (CONTROL ARM): Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * AFTER DAY +100 TEST RESULTS PATIENTS WITH LOW-RISK cGVHD (CONTROL ARM): Low serum/plasma levels of ST2, CXCL9, MMP-3, and OPN as indicated by low risk of chronic GVHD in the test results * AFTER DAY +100 TEST RESULTS PATIENTS WITH LOW-RISK cGVHD (CONTROL ARM): No use of ruxolitinib or other Jak inhibitors in the past 14 days * AFTER DAY +100 TEST RESULTS PATIENTS WITH LOW-RISK cGVHD (CONTROL ARM): Morphologic remission per day +100 bone marrow * AFTER DAY +100 TEST RESULTS PATIENTS WITH LOW-RISK cGVHD (CONTROL ARM): Adequate hematopoietic recovery (Hgb ≥ 8 g/dL, PLT ≥ 50K/ mm\^3) * AFTER DAY +100 TEST RESULTS PATIENTS WITH LOW-RISK cGVHD (CONTROL ARM): Negative serum or urine pregnancy test (female participants with childbearing potential only) * AFTER DAY +100 TEST RESULTS PATIENTS WITH LOW-RISK cGVHD (CONTROL ARM): Absence of active infection not responding to antibiotics * AFTER DAY +100 TEST RESULTS PATIENTS WITH LOW-RISK cGVHD (CONTROL ARM): Absence of progressive acute GVHD. Note: prednisone administration (flat dose of \< 0.25 mg/kg) is allowed. Patients receiving any other medication to control active/progressive GVHD will be excluded * AFTER DAY +100 TEST RESULTS PATIENTS WITH LOW-RISK cGVHD (CONTROL ARM): Absence of any clinically significant uncontrolled sickness Exclusion Criteria: * PRE-SCREENING: Prior chemotherapy \< 14 days prior to study biospecimen collection on day +100 post-HCT * PRE-SCREENING: Previous use of ruxolitinib or other JAK-inhibitors is allowed but administration should be stopped for at least 14 days prior to enrollment. Note: Previous use of Jak inhibitors before enrollment (including the pre-HCT period) should be recorded * PRE-SCREENING: History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent * PRE-SCREENING: Active/progressive acute GVHD at the time of screening. Prednisone administration (flat dose of \< 0.25 mg/kg) is allowed. Patients receiving any other medication to control active/progressive GVHD will be excluded * PRE-SCREENING: Patients with history of major adverse cardiovascular event (MACE)/other thrombosis (myocardial infarction \[MI\]/stroke and pulmonary embolism \[PE\]/deep vein thrombosis \[DVT\]) in the past 6 months * PRE-SCREENING: Patients with a history of tuberculosis * PRE-SCREENING: Clinically significant uncontrolled illness * PRE-SCREENING: Active infection not responding to antibiotics * PRE-SCREENING: Other active malignancy. Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * PRE-SCREENING: Females only: Pregnant or breastfeeding * PRE-SCREENING: Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * PRE-SCREENING: Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)