In the government's warped scale of values, an illegal alien who can establish her bona fides as a victim establishes herself as "special" on the track to a green card, with extra goodies thrown in while her case is pending. In short, it's better to have a black eye than a college degree.
Consider this recent explanation in English and Spanish: "How to get permanent residence in the U.S. if your spouse abuses you." (Extra points for a better photo caption than mine: "You paid WHAT for that lame manicure?")
The pitch is: "You may already be a victim! Just follow these simple directions."
Of course, government shouldn't have set up a system that practically invites fraud. Say a young wifey mail-ordered from some third-world hell hole grows tired of her possibly gray-haired citizen meal-ticket, er husband.
The correct governmental response should be protection from any actual violence and a free ticket home. Similarly, an immigrant male who is found to be beating up the girlfriend should be airmailed back to his place of origin.
Along the same line, foreign prostitutes who have been arrested but are willing to testify against their johns are eligible for an immediate raft of social services and eventual green cards. Why? Send those girls home to mama.