Dose a father have to get guardianship?

Ok so long story short! My husbands daughter recently got dropped off at our house by her mother. They lived in Tennessee, she was only there for 3 yrs. My husband had her before then. So she tells us shes coming up and wanted the daughter to stay with us for a day or two. Well it has been a lil over a month and we have not been able to get a hold of her! The number we have dint work. She told her daughter on facebook that she was done with her! She wants to sign over all right to us witch is fine! But, how do I go about it? Is it child abandonment cause I cant get a hold of her or do we just get a guardianship ? Looked everywhere for a good answer and cant find anything? Please help!