Dostoevsky's novel Crime and Punishment is really just one man's story--Raskolnikov's. Every other character in the novel is somehow connected to him, including his sister Dounia. She is younger than Raskolnikov and, like their mother, willing to make great sacrifices for him.
When we meet her, Dounia has just quit her position as a governess at the home of Arkady Ivanovich Svidrigailov because he has asked her to run off with him and his wife discovered his passion for Dounia. It is true that Dounia has no interest in the man except for the desire to somehow make him see the error of his ways; however, Svidrigailov is not so easily dissuaded. He probably murdered his wife (though it was ruled a tragic accident) and followed Dounia to St. Petersburg.
Dounia's brother is repulsed at the man when he first meets him, and that feeling is not much tempered throughout the novel. Svidrigailov assures Raskolnikov that what he felt for Dounia was a fleeting fancy and has passed, but later Svidrigailov traps Dounia and threatens to force himself on her when she does not want to come with him willingly. Though that does not appear to be love, he does eventually let her go before committing suicide. It is a warped love, but Svidrigailov loves Dounia, Raskolnikov's sister.