In other words, getting involved with violent men makes them feel stronger. They can then transcend feelings of vulnerability and poor self-appraisal. That much empowerment makes them feel more vital. Add the fantasy that they are truly loved or are being truly loving, and this connection can become an addictive drive.
A few of these women are also attracted to the celebrity status they gain—even if there is some dubious quality to it. They like going on talk shows to proclaim their love, being interviewed, and being allowed the chance to insist that the convicted murderer got a raw deal, was not capable of those crimes, or is different now. They may even take credit for "reforming" him, as if their love was the magical ingredient.
And the man doesn't have to be attractive. Henry Lee Lucas, a one-eyed serial killer who confessed to more than 300 murders, recanted, and confessed again, has had his share of female admirers. Despite his apparent sexual relationship with Ottis Toole, he's nevertheless compelling to some women as a potential mate. (One woman even came up with a plot to free him by posing as his supposedly murdered former girlfriend.)