Under a U-visa, you can obtain a visa if you have suffered physical or mental injury from a crime, and you have been, are, or will be helpful in the investigation or prosecution of that crime.

Officially, "U non-immigrant, humanitarian, material witness visas" include a provision so that you can get lawful permanent residency after 3 years. This is available even if you have never been married to your abuser, or if your abuser is not a US citizen or lawful permanent resident

Please read the more detailed information U Visa  Laws and Procedures.