Alemtuzumab in Myelodysplastic Syndrome (MDS), Aplastic Anemia, and T-Cell Large Granular Lymphocytic Leukemia (T-GL)

The Study Drug: Alemtuzumab is designed to attach to a protein that is found on certain immune cells, which may cause the cell to die. Study Drug Administration: If you are found to be eligible to take part in this study, you will receive alemtuzumab on Days 1-10 of one 28-day cycle. It will be given either by vein over 2 hours or by injection under the skin 1 time a day. Your doctor will tell you how the drug will be given. In order to get alemtuzumab provided for your treatment, the study staff will be filling out a form with your name and medical information (protected health information) for the company as part of the Campath Distribution Program. All participants will receive the same dose of alemtuzumab unless the starting dose causes intolerable side effects. If this happens, all future participants will receive a lower dose. Depending on your doctor's decision, to lower the risk of side effects you will receive Tylenol (acetaminophen) and Benadryl (diphenhydramine) or other drugs such as steroids (either by mouth or by a short infusion by vein), 30 minutes before each alemtuzumab dose. If you are receiving alemtuzumab and have chills during the infusion, you may receive Demerol (meperidine hydrochloride, a painkiller) to help control them. Starting on Day 1 and continuing at least 8 weeks after the last dose of study drug, you will be given 2 antibiotics to help fight infection. You will take Valacyclovir (or a similar drug) 1 time each day. You will take Trimethoprim/Sulfamethoxazole (or a similar drug) 2 times a day, 3 times per week. You will take both antibiotics by mouth. Study Visits: At Week 1: * You will have a physical exam, including measurement of your weight and vital signs. * Your performance status will be recorded. * Blood (about 1 tablespoon) will be drawn for routine tests. At Weeks 2-4, blood (about 1 tablespoon) will be drawn for routine tests. Beginning at Week 5 (+/- 3 days) and then 1 time monthly: * You will have a physical exam, including measurement of your weight and vital signs. * Your performance status will be recorded. * Blood (about 1 tablespoon) will be drawn for routine tests. At Week 12 (+/- 3 days) (end of the 3rd month), you will have a bone marrow aspiration and/or biopsy to test for chromosome abnormalities (if chromosomes were abnormal at screening) and to check the status of the disease. You may have additional bone marrow aspirations or biopsies if your doctor feels they are necessary. You will be asked about any side effects you may be having at each of your study visits. At any time during the study, if the doctor thinks it is needed, you will have a chest x-ray, a CT scan, or a PET scan to check the status of the disease. Length of Study: You will receive only one cycle of the study drug. Your participation on the study will be over after you have completed the end-of-study visit. You will be taken off study early if the disease gets worse or intolerable side effects occur. End-of Study-Visit: When you come off study you will have an end-of-study visit. At this visit, the following tests and procedures will be performed: * Blood (about 2 tablespoons) will be drawn for routine tests. * You will have a physical exam, including measurement of your vital signs. * Your performance status will be recorded. * You will have a bone marrow aspiration and/or biopsy to check for chromosome abnormalities, test for low levels of leukemia or lymphoma, to check the status of the disease, and molecular testing. Molecular tests are designed to look at the way the different parts of a cell (including DNA, RNA, and proteins) work together. * Blood (about 2 teaspoons) will be drawn to check levels of T-cells and immunoglobulins. This is an investigational study. Alemtuzumab is FDA-approved for the treatment of some patients with B-cell chronic lymphocytic leukemia (CLL). The use of alemtuzumab to treat MDS, aplastic anemia, or T-cell large granular lymphocytic leukemia is investigational. Up to 29 participants will take part in this study. All participants will be enrolled at MD Anderson.