Low-Dose Conditioning Followed by Donor Stem Cell Transplant in Treating Patients With Severe Systemic Sclerosis

Inclusion Criteria: 1. Patients with severe SSc as defined by the American College of Rheumatology and at high-risk for a fatal outcome based on the following prognostic factors from groups 1-5: * Group 1: Patients with 1) both a. and b. below; and 2) at least one of c., d. or e: * a. Diffuse cutaneous scleroderma with skin score of \>= 16 (modified Rodnan skin scale) * b. Duration of systemic sclerosis =\< 5 years from the onset of first non-Raynaud's symptom * c. Presence of interstitial lung disease with FVC or DLCOcorr =\< 70% of predicted and evidence of alveolitis (abnormal bronchoalveolar lavage \[BAL\] or high resolution chest computed tomography \[CT\] scan) * d. Left heart failure with left ventricular ejection Fraction (LVEF) \< 50% or pericardial effusion (mild-moderate) or 2nd or 3rd Atrial-Ventricular (AV) block; Myocardial disease not secondary to SSc must be excluded by a cardiologist * e. History of SSc-related renal disease that is not active at the time of screening; History of scleroderma hypertensive renal crisis is included in this criterion * Group 2: Patients will have progressive pulmonary disease as the primary indication for transplant as defined by a decrease in the FVC or DLCO by 15 percent or greater in the previous 12-month period. In addition, patients may have either less skin involvement than group 1 (mRSS \< 16) if they have a history of diffuse cutaneous disease and the FVC or DLCOcorr is \< 70% or both FVC and DLCOcorr \>= 70% if they have diffuse cutaneous disease (mRSS \> 16) at screening for the study; Patients must also have evidence of alveolitis as defined by abnormal chest CT or BAL * Group 3: Have progressive active SSc after prior autologous HCT based on the presence of progressive pulmonary disease; This will be defined by a decrease in the FVC since prior autologous transplant by 10 percent or greater, or DLCO since prior autologous transplant by 15 percent or greater in addition to evidence of alveolitis as defined by chest CT changes or BAL; If patients had prior autologous HCT on the SCOT clinical trial, they must have failed based on the defined study endpoints and be approved by the protocol principal investigator (PI) * Group 4: Patients who meet group 1 inclusion criteria but have FVC or DLCO \< 70% plus have had an adverse event to cyclophosphamide preventing its further use (i.e., hemorrhagic cystitis, leucopenia with WBC, 2000 or ANC \< 1000 or platelet count \< 100,000 and other adverse events) * Group 5: Diffuse scleroderma with disease duration =\< 2 years since development of first sign of skin thickening plus modified Rodnan skin score \>= 25 plus ESR \> 25 mm/1st hour and/or Hb \< 11 g/dL not explained by causes other than active scleroderma. 2. Unless patients have a DLCOcorr less than 45%, patients must have failed either oral or intravenous cyclophosphamide regimen defined as: * IV cyclophosphamide administration for \> 6 months or a total cumulative IV dose of 6 g/m\^2, or * oral cyclophosphamide administration for \> 6 months regardless of dose, or * combination of oral and IV cyclophosphamide for \> 6 months independent of dose 3. Patient must have a sibling who is a) HLA-identical and b) could serve as a donor of a peripheral blood stem cell graft to be placed on the transplant arm or an unrelated donor matched at HLA-A, B, C, DRB1 and DQB1. Patients without an HLA-identical sibling or an HLA-matched unrelated donor that meet the above criteria will be placed on the non-transplant arm DONOR: * The donor must be an HLA-identical sibling of the patient or an HLA-matched unrelated donor. * If the donor has reached the age of assent, then they must have completed the local institutional review board (IRB) assent process. * Donor must consent to G-CSF administration and to leukapheresis for HSC collection. * Donor must have adequate veins for leukapheresis or agree to placement of central venous catheter (femoral, subclavian). * Age 12-75 years; Pediatric donors must be \> 50 kg body weight. Exclusion Criteria: * Eligible for the NIH-sponsored randomized clinical trial (SCOT) * Fertile men or women unwilling to use contraceptive techniques during and for 12 months or until immunosuppression is discontinued following transplantation * Evidence of ongoing active infection * Pregnancy * Subjects with pulmonary, cardiac, hepatic, or renal impairment that would limit their ability to receive therapy and compromise their survival. This includes but is not restricted to, subjects with any of the following: * Severe pulmonary dysfunction defined as: 1. A hemoglobin corrected DLCOcorr \< 30% or FVC \< 40% of predicted; or 2. O2 saturation \< 92% at rest without supplemental oxygen; or 3. PO2 \< 70 mmHg or pCO2 \> 50 mmHg without supplemental oxygen * Significant uncontrolled pulmonary hypertension defined as: 1. Pulmonary artery peak systolic pressure \> 45 mmHg by echocardiogram and mean pulmonary artery pressure by right heart catheterization exceeding 32 mmHg at rest or 42 mm Hg during exercise; or 2. New York Heart Association (NYHA)/World Health Organization (WHO) classification for pulmonary hypertension, Class III or IV * Cardiac: Uncontrolled clinically significant arrhythmias; clinical evidence of significant cardiac disease (NYHA Class III or IV); LVEF \< 40% by echocardiogram * Significant renal pathology, defined as: 1. Estimated CrCl \< 60 mL/min (using Cockcroft-Gault formula based on actual body weight) or serum creatinine \> 2.0 mg/dL OR 2. Active, untreated SSc renal crisis at the time of enrollment * Active hepatitis or liver biopsy evidence of cirrhosis or periportal fibrosis. Total bilirubin \> 2.5 x the upper limit of normal (and not related to Gilbert's syndrome) and/or Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \> 4 x the upper limit of normal * Patients with poorly controlled hypertension * Patients whose life expectancy is severely limited by illness other than autoimmune disease * DONOR: * Identical twin of patient * Female donors who are pregnant (positive B-HCG) or breastfeeding * Infection with human immunodeficiency virus (HIV) or active viral hepatitis (B or C) * Known allergy to G-CSF * Current serious systemic illness * Uncontrolled bacterial, viral or fungal infection (currently taking medication and progression of clinical symptoms) * Donors receiving experimental therapy or investigational agents * Donors with cancer other than treated basal cell or carcinoma in situ of cervix; Cancer treated with curative intent \> 2 years previous will be reviewed on a case-by-case basis by a Protocol Chair or Medical Monitor