Usage patterns
〈事〉が終局を迎えるfor something to reach its conclusion
The long negotiations finally reached their conclusion.
対局が終局に入るfor a match (of go/shogi) to enter its endgame
The match between the two players finally entered its endgame.
〈事〉が終局するfor something to come to an end
The civil war came to an end several years later.
終局まで〈動詞〉to do something until the very end
He never gave up until the very end.