The hope is that one day stem cells can be used to cure many types of cancers. It impossible to predict what scientific and political developments will occur in the future, however, this is the goal of many researchers.
To answer your question--YES. Stem cells can, and in fact do right now, cure cancer. Currently, stem cell transplants are a widely used therapy for a few types of cancers. A stem cell cancer is a possible treatment for types of leukemias and lymphomas (both are blood cancers). The procedure is fraught with difficulties but works. Essentially what happens--the patient is given high dose chemotherapy
and / or radiation therapy to kill as many of the cancer cells as possible. The chemotherapy also clears out the bone marrow to make room for new stem cells, which are then injected into the patient. The stem cells are collected from healthy donors or even umbilical cords from healthy baby donors. The new stem cells then find a home in the marrow. These cells then attack the cancer cells that they see as foreign--thereby "curing" the patient of the cancer. There are many complications that can occur--but its is currently a successful process that is used.
As for it this will ever work for solid cancers, like stomach cancer--this is the hope. Research is actively being done in this area.
I encourage you to discuss your questions with your father's oncologist