Overstay of 11 years

My niece of Filipino parents was born here in New York. She was only months old with American passport when she went back to Philippines. My sister didn't get her a dual citizenship up to this moment. She's a single mom & can't afford the financial fees. My niece is now 11 years old with expired US passport. What should my sister do to fix my niece's papers in order for her to go back to US? How much would be the total fees for 11 years overstaying? Does my niece needs to get a dual citizenship?

According to what you posted here the child is US citizen by birth. The mother needs to apply for a new US passport for the child. Details including what documents, forms and fees are required are on travel.state.gov under the tab passport. If you need additional information please let us know.
There is no overstay on the US side. I do not know about the Filipino one.