As Large Language Models (LLMs) become increasingly prevalent, their generated outputs are proliferating across the web, risking a future where machine-generated content dilutes human-authored text. Since online data is the primary resource for LLM pre-training, subsequent models could be trained on an unknown portion of synthetic samples. This could lead to model collapse, a degenerative process whereby LLMs reinforce their own errors, reduce output diversity, and ultimately yield declining performance. In this study, we investigate the impact of decoding strategy on model collapse, analysing the text characteristics at each model generation, the similarity to human references, and the resulting model performance. Using the decoding strategies that lead to the most significant degradation, we evaluate model collapse in a more realistic scenario where the origin of the data (human or synthetic) is unknown. We train a machine-generated text detector and propose an importance resampling approach to prevent model collapse by up-sampling likely human content in the training data. Our method is validated on four LLMs from two model families (GPT-2 and SmolLM2), across a range of model sizes 124M to 1.7B). We demonstrate that it not only prevents model collapse but also improves performance compared to training on purely human data, underscoring the benefit of synthetic samples and the importance of data curation.