She learns that her father has escaped bail and has put the house up as a bond, although the Dolly family imminently risk losing it if the father doesn't turn up very soon. So Ree has to search for him by asking the sometimes violently hostile families that make up the community which inspired Daniel Woodrell's novel on which this movie is based.
It is Ree's uncle Teardrop, a crank addict who unexpectedly helps his niece, who leads to Ree re-securing her home. And although Teardrop's admission toward the end that he can no longer play banjo says much for the traditional mountain culture that is in danger of disappearance, the very end suggests - via the symbols of the newborn chicks and Ree's younger sister actually getting a better sound out of the banjo than Teardrop - that there may still be hope.
Winter's Bone is Debra Granik's second movie: her first - Down to the Bone (2004) - concerns a married, working-class mother of two in upstate New York, who is secretly addicted to cocaine. A Guardian article on the female movie directors Granik, Nanette Burstein, and Sanaa Hamri is here.
Addendum: I've just discovered this article from Southern Spaces: 'Life in a Shatter Zone: Debra Granik's Film Winter's Bone'.