Needy; fallen on hard times. Men's shoes have two parts: the bottoms (soles and heels) and the uppers, which cover the foot. Someone whose financial condition was so bad that he couldn't afford to have the soles and heels replaced after being worn away was literally down on (in the sense of “to”) his uppers. A similar phrase is “down at the heels,” and moving higher, “out at the elbows.”