What to do with an abandoned child?

A woman and her nine yr old child have been staying with my mother, they are homeless and have been since mother's day. She has only been staying with my mom for about a week. The landlord said they needed to be out within the next couple of days. The mother told her daughter yesterday morning around 10am she would be back within 20 min and no one has seen or heard from her since... 31 hours later. My mother just wants to ride it out and wait for her to come back. I think she should turn it in. So she can't be held liable. What's the right thing to do here? I'm torn.