The Awful Truth
Evelyn Mulwray is a woman with a mysterious past… and it turns out it's not only a mysterious past, but an extremely sad, twisted, and horrible one. We wait for much of the movie to discover what exactly this past is—and, when we finally do, it's super shocking:
Evelyn and her father, Noah, conceived a child together. Now Evelyn's trying to escape Noah's clutches, running away with her sister/daughter, who's nearly grown to adulthood.
Ugh. Who in the audience was expecting incest to suddenly come up in this movie about water theft and corruption?
Of course in retrospect, there were some hints. At one point, Jake asks her about her father, to Evelyn's obvious discomfort:
GITTES: Is there something upsetting about my asking about your father?
EVELYN: No!... Yes, a little. You see Hollis and my fa—my father had a falling out...
GITTES: Over the water department—or over you?
EVELYN: Not over me. Why would they have a falling out over me?
Oh, Evelyn. You doth protest too much. Jake's thinking about normal father/son-in-law arguments…but Evelyn's mind is on something much, much darker.
Jake has no reason to suspect her father of committing incest with her, but Evelyn is already nervous that he might catch on—which is a wee bit suspicious. Unfortunately, Jake doesn't catch on for a long time. When Evelyn hesitates to admit that the girl her husband Hollis Mulwray was visiting was actually her sister, Jake can't understand why she's so tense.
Hindsight's 20/20, Gittes.
At first, Evelyn is presented as a mystery to Jake and to the audience. We don't really get a lot of insight into her character until later in the movie—since understanding her character and her situation at the beginning would ruin all the suspense if it were divulged too soon. We can see that she's hiding something, though.
She quickly—too quickly— dismisses any threat of a lawsuit against Jake after he accidentally frames her husband for adultery.
Naturally, this makes Jake—and the audience—understand that something fishy's going on. We think that maybe she killed her husband…but she dismisses the idea, claiming that she wasn't sleeping with him anymore, and that she was free to have affairs herself. And, even though he still doesn't understand her, Jake ends up sleeping with her, shortly after he's unraveled the retirement home aspect of Noah Cross's plan to steal water.
When Jake discovers that Evelyn's hiding the woman her husband was supposedly having an affair with, he thinks that Evelyn's kidnapped her and drugged her in order to prevent her from telling the truth about how and why Hollis Mulwray was killed.
This is a total misreading of the situation…and of Evelyn. Jake hasn't picked up on Evelyn's hints, like when she'd told him earlier (after they had sex):
EVELYN: I want you to listen to me—my father is a very dangerous man. You don't know how dangerous. You don't know how crazy.
But Jake doesn't fully understand the hint—he still doesn't have enough info.
We finally learn the truth about Evelyn when Jake confronts her and accuses her of holding Hollis's mistress captive. He slaps her multiple times, while Evelyn says first, "She's my sister" and then "She's my daughter." Then, the awful reality comes out:
EVELYN: She's my sister and my daughter!
Evelyn explains that when she was just fifteen years old, her father had sex with her—when Jake asks "Did he rape you?" she shakes her head no, but legally it would certainly be considered rape.
Now, she wants to escape with her daughter, preventing her father from further destroying their lives. Of course, it all ends tragically: her father tracks her down to Chinatown, where she tries to shoot him, but fails to cause a serious injury. The cops shoot and kill Evelyn, and Cross carries his daughter/granddaughter away from the scene.
(No: this ain't an ending that gives you the warm fuzzies.)
But, still, Evelyn behaves with real courage, both for herself and for her daughter. She doesn't remain cowed by Noah—after all, she tries to kill him. Her tragedy is that she dies and her daughter gets stolen, but at least she still has a "seize the sword" moment.
By contrast, Jake's "seize the sword moment" gets stolen from him, and he's never able to gain control over the chaos in the final scene or really take on the bad guys. So, we're left feeling bad for Evelyn…but we're also left admiring her too.