He understood that his death was imminent, but wished to be treated anyway. According to Christian Shephard, he had an inoperable spinal tumor and was not a candidate for surgery: "What he is looking for is a miracle."
Jack attempted surgery, inspired by the "miracle" of Sarah's recovery. The surgery failed and Angelo died on the operating table.
In the Italian-language broadcast, Angelo Busoni and his daughter speak French, as all characters speak Italian in that dub.