Brief Summary: This phase II trial studies the outcomes of using a JAK inhibitor prior to reduced intensity haploidentical (Haplo) transplantation for the treatment of primary or secondary myelofibrosis (MF). Haplo transplant has been shown to be safe and effective in patients with leukemia and lymphoma who don't have an available sibling donor. The primary risk of using Haplo HCT in patients with MF is graft failure as the graft failure rate has been historically higher with Haplo HCT than with other donor sources and higher with MF patients due to bone marrow fibrosis than in patients with other hematologic malignancies. JAK inhibitors when used in patients with MF may decrease the size of the spleen and decrease inflammation in the bone marrow. Therefore using a JAK inhibitor prior to Haplo transplant has the potential to decrease graft failure in patients with MF. Haplo transplants for patients with MF have been done successfully at multiple institutions in patients not on a study and are currently being covered by Medicare.

Detailed Description: OUTLINE: JAK INHIBITOR THERAPY: Patients receive a JAK inhibitor at least 8 weeks prior to the start of hematopoietic cell transplantation (HCT) conditioning through day -4 before transplantation. CONDITIONING: Patients receive melphalan intravenously (IV) over 1 hour on day -5, fludarabine IV over 30-60 minutes on days -5 to -2, and undergo total-body irradiation (TBI) on day -1 or day -1 and day 0. TRANSPLANT: Patients receive peripheral blood stem cell infusion on day 0. GVHD PROPHYLAXIS: Patients then receive cyclophosphamide IV over 3 hours on days 3-4, tacrolimus IV beginning day 5 then orally (PO) for 6 months, mycophenolate mofetil PO twice daily (BID) or three times daily (TID) beginning day 5 for 6 weeks, and granulocyte colony-stimulating factor (G-CSF) subcutaneously (SC) beginning day 7 until neutrophil recovery is \> 1,500/mm\^3. All patients undergo magnetic resonance imaging (MRI), computed tomography (CT), bone marrow biopsy and aspiration and blood sample collection throughout the trial. Patients also undergo echocardiography (ECHO) or multigated acquisition scan (MUGA) on the trial. After completion of study treatment, patients are followed up between day 80-100, at 1 year, and then up to 5 years.