Cancers main pathway for growth is via sugar fermentation, because the mitochondria in cancer cells don't function like normal, healthy, mitochondria. So if you don't eat sugar for a long period of time tumor growth can and will stall and begin to shrink as the cancer is starved. Dr. Thomas Seyfried has done a lot of work on this topic, and almost all his research is free and available to access via PubMed. Allegedly in some cases he saw patients who had Glioblastoma tumors, one of the deadliest forms of brain cancer, stop growing, shrink and clear up entirely after patients started a ketogenic diet.