This guidance from the Social Security Administration, available in English and Spanish, reviews the process for victims of domestic violence to obtain a new social security number.
"Although we don’t routinely assign new numbers, we’ll do so when evidence shows you are being harassed or abused, or your life is endangered. Applying for a new number is a big decision. Your ability to interact with federal and state agencies, employers, and others may be affected. Your financial, medical, employment, and other records will be under your former SSN and name (if you change your name). If you expect to change your name, please do so before applying for a new number."