Every cancer cell line is unstable chromosomally. Beside cancer cells are usually unstable , the culture conditions may exert further factors to make them unstable more.
Nahi is true: cancer cell lines are unstable. Maybe if you use lymphoma or myeloma cell lines you can previously characterize their karyotype and then start your experiments. The thing is that it will be difficult to determine if karyotype changes are due to your treatment or to the cell line's own instability.