We know foils are supposed to come in pairs, but these women form a foil trio. Raskolnikov is always lumping them together in his mind as abused women who he has to save. They are all three characterized by religious devotion, selflessness, and sacrifice. The various degrees of strength, outsider-ness, and helplessness are in a constant state of compare and contrast. When Raskolnikov kills Lizaveta when he means to help her, it calls into question and literally hinders his ability to help the other two. In some ways he learns that he isn't the great savior, doesn't have all the answers, and that maybe he's the one who needs help. Also, when Dounia and Sonia become friends before Sonia and Raskolnikov leave for Siberia, Lizaveta is the link between them. They must simultaneously mourn her and forgive Raskolnikov.
Raskolnikov's bad qualities pale by comparison to Svidrigaïlov's. That Raskolnikov is able to live and find happiness emphasizes Svidrigaïlov's inability to do so. One man is forgiven; one man commits suicide. You see how this foil thing works.
By the end of the book, both Raskolnikov's mother and Sonia's stepmother are dead. They are both plagued by psychological problems before they die. They are both widows. They both consider themselves fine ladies, and can both be a bit snobbish. In Pulcheria we see this in her treatment of Sonia, in Katerina in her treatment of foreigners. In Raskolnikov's mind Pulcheria is forcing Dounia into prostitution, just like Katerina did Dounia, by allowing her to marry Luzhin.
On the other hand, Pulcheria is basically calm and dignified. We can't imagine her making scenes in public, physically abusing her children, driving her daughter to prostitution (even a stepdaughter), or committing any violent act. She has financial problems, but they are nothing compared to Katerina's. Together, these two women make for interesting foils.