to come up against someone or something: to meet, to confront, or (of an event) to befall
At its core this word pictures one party coming up to face another. The same picture covers a friendly approach (running out to greet an arriving guest), a hostile approach (marching out to confront an enemy in battle), and even an event coming upon a person (a disaster that overtakes them). Almost always the word travels with the little phrase that means "to meet" or "toward," and in story after story it sets up the moment two parties come face to face.
Whether the meeting is warm or deadly is decided by the surrounding words, not by this verb itself. The patriarchs run out to embrace returning kin with it; armies use the very same expression to march out for war. That neutrality is the point: the word names the encounter, and the scene supplies the mood.
When the one who comes up is not a person but a fate, the verb shifts smoothly to "befall" or "happen to." Harm befalls a son, evil overtakes a people, dread comes upon a man in the night. It is still the same image of something advancing to meet you, only now what advances is an event rather than a face.
This word should not be confused with the look-alike verb for calling out or naming, which is spelled the same in some forms but is a separate word.