Yes, it is possible to survive stage IV cancer that has spread. People are individuals and not statistics. No one knows what will happen to your aunt. Stage IV is difficult to treat but it can be done and there are survivors . . no one, not even a doctor, can know if your aunt will or will not be one of them.
I know survivors of advanced abdominal cancers . . no one could have predicted they would survive their cancer, but they did . . most of them underwent high dose chemotherapy for many months, extensive surgical debulking (often two surgeries to complete) stem cell transplant (or hyperthermic chemoperfusion) followed by whole abdominal radiation and adjuvant chemotherapy . . two of the survivors had extensive ovarian disease.
I would suggest that your aunt join an online support group and ask questions of other advanced cancer patients who have survived a long time. It is also possible that even if the disease is not 'cured' that your aunt could find a treatment that will allow her to live with the cancer by controlling disease progression.
Your aunt should try to contact the following groups:
ACOR: Ovarian Cancer ListServ
ACOR: The Gynecological Cancers Online Support Group
Ovarian Cancer National Alliance
There are many other resources out there that are far better than any 'advice' you might seek out here . . use them. good luck to your aunt.
Stage 4 means it has spread and the fact that it is in her stomach and her lungs is evidence that it has. Stage 4 is not considered curable and has a 5 year survival rate of 10%. Very few go on to live long normal lifetimes.