Someone who is still living, even after the death of another or the end of a situation or event, is said to be surviving. For example, if a person dies, the husband or wife is "the surviving spouse."
The Greek philosopher Epicurus said, "You don't develop courage by being happy in your relationships every day. You develop it by surviving difficult times and challenging adversity." The word surviving is the adjectival form of the verb survive, which comes from the Latin vivere, "to live," plus the prefix super-, "over, beyond." The surviving person is the one who manages to go on living after another's death. The word has a legal importance, in that a surviving person may be an heir.