Yes, a female can develop tumors during pregnancy. The outside cells of the developing embryo in a pregnant female get converted into placenta that is responsible for providing nutrition to the developing fetus. These cells are called trophoblast cells. The rare group of tumors that form out of these cells are collectively named Gestational Trophoblastic Disease. These usually occur during pregnancy but some can occur some months after the pregnancy. It can be cured even if it is cancerous.