Is it possible for a benign breast tumor become cancerous?

Depends: Most benign breast lesions do not become cancerous. Some benign cell types like atypical hyperplasia or lobular neoplasua can indicate increased future risks of breast cancer. Need to know more about the cell type you are describing.

Rarely: It is uncommon for a proven benign tumor to become cancerous. But any change in size requires confirmation with a biopsy. The proof of cancer lies in biopsy and pathology examination under the microscope!

Depends on : Which benign tumor. Fibroadenomas, the most common kind, do not become malignant until they become very large. Some other types, though, can undergo malignant transformation. So it is best to get them removed to know what kind of benign tumor.