If my nephew has been living with me since June 2015, her mother has little to no contact with him, can her mother get him back?

My nephew has been living with me since June 2015, his mom signed papers transferring him to my food stamps and medical in October 2015. Since then I was also put in charge of his education. I applied for cash aid April 2017 and they opened a case with child support. She was served with the questionnaire 2 days ago and was very upset. She was threatening to take him back with her. She has little to no contact with her son, he is 16 now. And I invite her over all the time trying to get her to spend time with him. She never pays for anything. And she refuses to sign over guardianship or custody because she still receives child support for him from his father. (He has no custody or visitation). I was wondering if she can take him home, given he is 16.