The Forger (2011) on Netflix

Plot summary

Joshua Mason, fifteen, is on his own in Carmel-by-the-Sea, California, after his mother leaves him at a motel. He sells a painting he finished at a local mission, and when the manager demands payment he runs, leaving the drawings that fill his room behind for social worker Vanessa Reese to find. Joshua befriends a girl named Amber, and after he pulls a school employee off her, her brother Ryan confronts him. While he waits out the rain in a culvert, water sweeps him into the ocean and hurts his hand. He lets himself into a seaside mansion by an unlocked side door, cleans the wound, eats, and finishes an unfinished portrait in the art studio before falling asleep. The owner, Everly, impressed by how the boy completed the painting, decides to take him in.