We demonstrate that error correcting codes (ECCs) can be used to construct a labeled data set for finetuning of "trainable" communication systems without sacrificing resources for the transmission of known symbols. This enables adaptive systems, which can be trained on-the-fly to compensate for slow fluctuations in channel conditions or varying hardware impairments. We examine the influence of corrupted training data and show that it is crucial to train based on correct labels. The proposed method can be applied to fully end-to-end trained communication systems (autoencoders) as well as systems with only some trainable components. This is exemplified by extending a conventional OFDM system with a trainable pre-equalizer neural network (NN) that can be optimized at run time.