Jackie always had a weakness for Jenny and protected her in the orphanage, often taking a beating for her. When she realized Jackie was a hit-man and bearer of the Darkness she left Jackie. It was too painful for her to look at Jackie living his life this way, especially since she had feelings for him.
Jenny appears in the video game version of The Darkness. She is Jackie's girlfriend ever since they were in the same orphanage as kids. They even celebrated his 21st birthday. Jackie tries to tell Jenny that he is a hit-man working for Uncle Paulie, but she doesn't believe him. Later, she is kidnapped by Paulie and a crooked cop, Captain Eddie Shrote, and is taken in the same orphanage where she and Jackie used to go. While on a mission to rescue her, the Darkness holds Jackie back from doing the rescue, giving Paulie a chance to kill her in front of him. Before she died, Jenny said to Jackie that it is not his fault they got into this situation.
Jenny returns in The Darkness II , once again as an illusion used to torment Jackie. She also appears as a nurse in a mental hospital in Jackie's Institution, (a place where he is sent while the Darkness repairs him from fatal injuries). In this world, Jackie is clinically insane and only thinks he is a mob boss, and is infatuated with Nurse Jenny, who does not feel the same. The actual Jenny reappears later as The Darkness reveals he is holding her soul hostage and uses this as leverage to force Jackie to cooperate throughout the game, near the end of the game she is freed, and depending on what choices you make. You can stay with fake Jenny in the otherworld Institution, and dance with her until the game ends or you can travel to within The Darkness to save her.
If you save her, after kissing and hugging, it is eventually revealed she is the new host of the Angelus explaining why The Darkness contained her there. After the Angelus emerges, it yells at Jackie for being "too powerful of a host" and flies off, leaving Jackie and the Darkness in the Abyss within Hell.