Clofarabine is approved by the FDA for the treatment of pediatric patients (1 to 21 years of age) with relapsed or refractory ALL. Alemtuzumab is approved by the FDA for treatment of B-cell chronic lymphocytic leukemia (B-CLL) in patients over the age of 18. These drugs have been used to treat patients with leukemia in other research studies like this one. Both drugs have individually been administered to adult patients with ALL with acceptable toxicity profiles. This study will evaluate the combination of clofarabine and alemtuzumab when administered to adult patients with relapsed or refractory ALL. Primary objectives of the study is to determine the maximum tolerated dose of clofarabine when administered with alemtuzumab, evaluate the safety of the combination, and assess for activity of the combination by evaluating response rate, effect on ALL progenitor cell population, and patients who are able to bridge to transplant.