Poor Winky is a classic house-elf. She's a loyal servant attached to a single wizarding family. The problem is that she belongs to the Crouch family, which is divided against itself. So who should she be loyal to, the son or the father? She tries to help both all at once and thus winds up being the tool to destroy the whole family.
Hurting More Than Helping
We first see Winky when she's holding a seat for Mr. Crouch at the Quidditch World Cup. Of course, what she's really doing is accompanying Barty Crouch, Jr. to the game while he hides under an Invisibility Cloak. It's Winky who arranges this whole outing: "She spent months persuading [Mr. Crouch]" (35.139) to let Barty Crouch, Jr. have an outing.
But while Barty Crouch, Jr. is sitting in the stands, his mind clears and he steals a wand from a boy who happens to be sitting in front of him (Harry!). Winky notices that he's starting to come to himself so she hurriedly drags him away from the crowd. However, Barty Crouch, Jr. breaks free and casts the Dark Mark into the sky, terrifying all the wizards who have gathered there for the World Cup.
Representatives of the Ministry of Magic (including Mr. Crouch) find Winky standing in the forest with the wand she took from Barty Crouch, Jr. Everyone thinks it's because Mr. Crouch is ashamed that Winky has been associated with the Dark Mark that he dismisses her. But, in reality, it's because she's let Barty Crouch, Jr. go. Even though she was supposed to watch the guy, his son has gotten away.
Mr. Crouch manages to recapture Barty Crouch, Jr. (who has been stunned), and he brings him back home. Now it's just Mr. Crouch and his son alone in their house, and Voldemort knows that Barty Crouch, Jr. is alive, thanks to Bertha Jorkins. So, when Voldemort arrives, Mr. Crouch has no defense. He's kept as a prisoner under the Imperius Curse in his own home. Anyway, this isn't about Mr. Crouch. We are just pointing out that, by firing Winky for betraying him, Mr. Crouch in fact leaves himself even more vulnerable to Voldemort.
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Homeless / Identity-less
Once she has been fired, Winky goes into a sharp decline. Dobby, the kindly elf who has befriended Harry, gets her a job in the Hogwarts kitchens. But she begins drinking, and she weeps regularly at the thought of the Crouch family. She worries particularly about Mr. Crouch, since she's heard that he is ill. Winky exclaims that she's "properly ashamed of being freed!" (21.143). In other words, Winky is like a counterexample to Dobby. Dobby was eager to leave the Malfoy family, and he's pleased to be getting paid to work now. On the other hand, Winky feels that she's "a disgraced elf" (21.143), and she can't come back from that. Whenever Hermione starts talking about S.P.E.W., all she has to do is look at Winky to see a negative example of what freedom does to a house-elf.
Perhaps the most tragic part of the whole Winky disaster is at the end of the novel, when she runs to her "Master Barty" (35.125) – Barty Crouch, Jr. Even as Barty Crouch, Jr. starts confessing all of these terrible things he has done, Winky weeps and tries to excuse him and begs him to be quiet.
Finally, when Barty Crouch, Jr. admits that he killed his father, Winky wails: "Noooo! [...] Master Barty, Master Barty, what is you saying?" (35.164). All Winky can do is cry at this point. What is she supposed to think? She's fiercely devoted to both Barty Crouch, Jr. and Sr., and now she knows that the former murdered the latter, in part because of her interference. If house-elves were less closely bound to their wizard families, maybe she could have done something different. Even though we think Hermione goes too far with her unrelenting S.P.E.W. politics, that doesn't mean we think there's nothing wrong with the house-elf system. After all, look what it's done to both Dobby and Winky!