The Cubs were one game away from winning the World Series in 1945 (they lost 4 games to 3 to Detroit). That’s the last time they played in the World Series, although they almost made it in 1984 (when they would have had a chance to lose to the Tigers again—San Diego lost 4 games to 1).
The Cubs were one game away from winning the World Series in 1945 . . .. . . and the Texas Rangers twice were a strike away from winning the Series in 2011.
Close counts only in horseshoes, hand grenades, and (I think) atomic bombs . . . unfortunately.