This phase II trial studies how well pioglitazone hydrochloride and tyrosine kinase inhibitor (TKI) therapy works in treating patients with chronic myeloid leukemia (CML) that has come back after a period of improvement (relapsed) after a first TKI discontinuation. TKI may stop the growth of cancer cells by blocking certain enzymes need for cell growth. Although TKI therapies are effective against CML, there are residual cancer cells called leukemia stem cells that are able to hide from TKIs. Pioglitazone is a drug approved by the Food and Drug Administration to treat diabetes and has been shown in laboratory studies to increase CML stem cell death when given together with TKI therapy. Giving pioglitazone with TKI therapy may be effective in treating patients with CML.