In 2012, Dagan was diagnosed with liver cancer, and began chemotherapy treatment, but the cancer spread and he began to suffer from liver failure. In October of that year, he flew to Belarus and had a successful liver transplant operation performed by French-Jewish surgeon Daniel Azoulay, considered one of the world's leading liver transplant surgeons. After the operation, he was admitted to an isolation unit for fear of infection. At the time, criteria for a liver transplant in Israel dictated the patient must be no older than 65, so the 67-year-old Dagan had to seek treatment abroad. Israeli Foreign Minister Avigdor Lieberman helped facilitate the operation. On 27 October 2012, after his condition had stabilized, Dagan returned to Israel and was immediately hospitalized. He was discharged from Ichilov Hospital and began recuperating. Dagan was accompanied throughout his ordeal by Rabbi Avraham Elimelech Firer, with whom he developed a close relationship, and later reciprocated by helping Firer raise funds for a new rehabilitation center.
