On many passenger manifests, if Ancestry or family search includes an image, the passenger had to name someone still in the "old country" who would be notified if a disaster or death occured and note what the relationship was to the passenger.
Clues may be found also by noting on other passenger lists, immigrants of the same surname from the same area and on USA census records, those of the same surname living in the same city area. Frequently, an elder brother would come to the USA, earn money and send for other family members - siblings, parents, etc