Data cleaning often comprises outlier detection and data repair. Systematic errors result from nearly deterministic transformations that occur repeatedly in the data, e.g. specific image pixels being set to default values or watermarks. Consequently, models with enough capacity easily overfit to these errors, making detection and repair difficult. Seeing as a systematic outlier is a combination of patterns of a clean instance and systematic error patterns, our main insight is that inliers can be modelled by a smaller representation (subspace) in a model than outliers. By exploiting this, we propose Clean Subspace Variational Autoencoder (CLSVAE), a novel semi-supervised model for detection and automated repair of systematic errors. The main idea is to partition the latent space and model inlier and outlier patterns separately. CLSVAE is effective with much less labelled data compared to previous related models, often with less than 2% of the data. We provide experiments using three image datasets in scenarios with different levels of corruption and labelled set sizes, comparing to relevant baselines. CLSVAE provides superior repairs without human intervention, e.g. with just 0.25% of labelled data we see a relative error decrease of 58% compared to the closest baseline.