It is absolutely possible, but usually requires some kind of third-party assistance, like individual or group therapy, or the close and constant support of a friend. It's important to understand where the inclination to date these people comes from -- something from the person's childhood? a psychological desire that hasn't found another way to manifest itself? -- and what triggers the abused person's interest to continue entering into relationships with them. What does it feel like they're providing the person with? Where else can the person get that feeling that is more healthy? These are just very superficial questions that he/she (the abused) may want to start with. I highly recommend getting outside help from a professional who will assist him/her in asking and answering these questions, and potentially facing some very frustrating/scary/difficult truths about him/herself.
Most importantly though, the abused individual needs to remember and know that he/she doesn't DESERVE abusive behavior, and it can change.