The answer requires much more information. How is the title of the house held? Did you contribute value to have your name on the title of the house? Why is the house in both names? Do you live with your mother? Have you provided care to your mother such as has kept her out of a nursing home for at least two years? Have you a disability?
Agencies don't "take" property, they declare the applicant for benefits ineligible because of improper transfer of assets. Government agencies have certain rights to file liens against property or claims against the estate of persons who have received benefits from them.
You really need to consult with a local elder law attorney. This can't be fully answered over the Internet.
It sounds like your mother has been guessing about what to do. She needs to consult with a lawyer before she makes a costly mistake.
Similar to the previous answer, more information is required. However, in Pennsylvania the home cannot be taken by the Dept. of Public Welfare while your mother is living. If she requires medical assistance for nursing home care, a detailed review or application of her assets and income is required. She may or may not qualify for such medical assistance for some period of time depending on the outcome of this application and review of assets and income. The Dept. of Public Welfare may have a claim after your mother dies for what is called "estate recovery" - in essence, DPW can seek to be reimbursed in part for the cost of medical assistance (nursing home care) for your mother. Also, you mention that the home has been in your name and her name for seven years. It may be possible to transfer the entire interest in the house to you. This requires analysis to see if such a transfer meets with the DPW regulations re: your mother's ability to qualify timely for medical assistance for nursing home care. We would want to see the Deed to determine just what "legal language" was used when the deed was put in both names. Do you live in the house? why? what is the value of the home? Is she in a nursing home already? or an assisted care facility? or is she still living in the house? These are some of the questions that need to be looked at to properly answer your question.