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We extend evidence-aware claim verification to the context of positive-unlabeled (PU) learning. Existing works assume the truth and the falsity of the claims are known for training and form the task as a supervised learning problem. However, this assumption underestimates the difficulty of collecting false claims; we argue that claim verification is more challenging in the absence of negative labels. We consider a more practical setting, where only a comparatively small number of true claims are labeled and more claims remain unlabeled. Thus, we formulate the claim verification task as a PU learning problem. We decouple learning representation of claim-evidence pair from PU learning and adopt a pre-trained universal language model to encode claim-evidence pairs. We further propose to use the generative adversarial network (GAN) to capture the latent alignment between encoded claim-evidence pair and the truthfulness. We leverage the verification as part of the GAN by extending previous GAN based PU learning. We show that the proposed model achieves the best performance with a small amount of labeled data and is robust to the truthfulness prior estimation. We conduct a thorough analysis of the model selection. The proposed approach performs the best under two practical scenarios: (i) the unlabeled data is more than the labeled data; (ii) and the unlabeled positive data is more than the unlabeled negative data.