The problem of inducing a model for forecasting the outcome of an ongoing process instance from historical log traces has attracted notable attention in the field of Process Mining. Approaches based on deep neural networks have become popular in this context, as a more effective alternative to previous feature-based outcome-prediction methods. However, these approaches rely on a pure supervised learning scheme, and unfit many real-life scenarios where the outcome of (fully unfolded) training traces must be provided by experts. Indeed, since in such a scenario only a small amount of labeled traces are usually given, there is a risk that an inaccurate or overfitting model is discovered. To overcome these issues, a novel outcome-discovery approach is proposed here, which leverages a fine-tuning strategy that learns general-enough trace representations from unlabelled log traces, which are then reused (and adapted) in the discovery of the outcome predictor. Results on real-life data confirmed that our proposal makes a more effective and robust solution for label-scarcity scenarios than current outcome-prediction methods.