This work investigates the limits of communication over a noisy channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless binary-input channel and when the number of transmitted ones causes a sufficient amount of damage, the channel ceases to convey signals. We restrict attention to constant composition codes. Since infinite blocklength codes will always wear out the channel for any finite threshold of failure and therefore convey no information, we analyze the performance of finite blocklength codes to determine the maximum expected transmission volume at a given level of average error probability. We show that this maximization problem has a recursive form and can be solved by dynamic programming. A discussion of damage state feedback in channels that wear out is also provided. Numerical results show that a sequence of block codes is preferred to a single block code for streaming sources.