The authors introduce a new notion, sustainability, in bankruptcy problems. An agent \(i\)'s claim is sustainable if it is so small that if no other agent has a larger claim then there will be enough to cover all the demands. The sustainability condition requires that such small claims should be fully honored. Path independence requires that, when the worth of the estate is lower than what was expected, the initial solution, once adjusted, or the new solution to the actual problem give the same answer. The authors show that the constrained equal-awards rule is the only rule that satisfies path independence and sustainability. Using duality, the constrained equallosses rule is also characterized.