Erythropoietin (EPO) suppresses drug-induced apoptosis in EPO-receptor-positive leukemia cells and allows cells to persist after drug treatment by promoting cellular senescence. Importantly a small proportion of senescent cells can re-enter the cell cycle and resume proliferation after drug treatment, resulting in disease recurrence/persistence. Using a single-cell assay to track individual cells that exit a drug-induced senescence-like state, we show that cells exhibit asynchronous exit from a senescent-like state, and display different rates of proliferation. Escaped cells retain sensitivity to drug treatment, but display inter-clonal variability. We also find heterogeneity in gene expression with some of the escaped clones retaining senescence-associated gene expression. Senescent leukemia cells exhibit changes in gene expression that affect metabolism and senescence-associated secretory phenotype (SASP)-related genes. Herein, we generate a senescence gene signature and show that this signature is a prognostic marker of worse overall survival in AML and multiple other cancers. A portion of senescent leukemia cells depend on lysosome activity; chloroquine, an inhibitor of lysosome activity, promotes senolysis of some senescent leukemia cells. Our study indicates that the serious risks associated with the use of erythropoietin-stimulating agents (ESAs) in anemic cancer patients may be attributed to their ability to promote drug-tolerant cancer cells through the senescence program.