Another example is encrypted data. Statistically, encrypted data is indistinguishable from random. Truly random data is impossible to compress losslessly. But

Another example is encrypted data. Statistically, encrypted data is indistinguishable from random. Truly random data is impossible to compress losslessly. But if you had a predictor so smart that it could crack the encryption key, it could start predicting the rest of the encrypted stream, and therefore compress it.