A sequence of outputs from a stationary memoryless source is encoded into n code streams sent over n parallel channels. Any k or fewer of these channels may have broken down, unbeknown to the encoder. The receiver maps the streams from the surviving channels into a reconstruction sequence for minimum distortion. This distortion will take different values depending on what subset of channels is operative. Let D <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</inf> be the largest of these values, the worst-case distortion. This paper shows that the infimum of D <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</inf> over all encodings is the same as if the encoder did have knowledge of the breakdown situation.