The movie's named after the Amtrak route that runs from Chicago to Seattle. Sheil's character boards it about a third of the way into the movie to visit her family's cabin in Montana. Her businessman husband, played by Swanberg's husband, Joe, plans to drive out there later on. It's unclear what he does for a living, except that it pays for their nice high-rise apartment and the work keeps him very busy. He's the sort of passive-aggressive type that Joe (on the basis of performances he's given elsewhere) seems to know very well. Most of the conversations he has with his wife culminate with him steering her behavior under the pretense of compromise, much like a corporate office manager will profess interest in teamwork before telling his or her underlings what to do.
None of this seems to bother her much. As Swanberg presents her, the wife has gotten very good at letting life wash over her. Numerous scenes consist of long takes of Sheil simply going through the motions of domesticity: cooking, taking her infant for walks, tidying up the cabin. It's hard to feel sorry for someone so disengaged from her own life, but that seems to be the point. (The role must have been a challenge for Sheil: How do you convey chronic disinterest without seeming dull?)
Like Herr R., Empire hinges on a plot twist that's best not to know before going in. Suffice it to say, it gives the narrative an elegant symmetry and seems inevitable in hindsight.