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Face recognition systems are widely deployed for biometric authentication. Despite this, it is well-known that, without any safeguards, face recognition systems are highly vulnerable to presentation attacks. In response to this security issue, several promising methods for detecting presentation attacks have been proposed which show high performance on existing benchmarks. However, an ongoing challenge is the generalization of presentation attack detection methods to unseen and new attack types. To this end, we propose a new T-shirt Face Presentation Attack (TFPA) database of 1,608 T-shirt attacks using 100 unique presentation attack instruments. In an extensive evaluation, we show that this type of attack can compromise the security of face recognition systems and that some state-of-the-art attack detection mechanisms trained on popular benchmarks fail to robustly generalize to the new attacks. Further, we propose three new methods for detecting T-shirt attack images, one which relies on the statistical differences between depth maps of bona fide images and T-shirt attacks, an anomaly detection approach trained on features only extracted from bona fide RGB images, and a fusion approach which achieves competitive detection performance.