Personalized text-to-image models allow users to generate images of new concepts from several reference photos, thereby leading to critical concerns regarding civil privacy. Although several anti-personalization techniques have been developed, these methods typically assume that defenders can afford to design a privacy cloak corresponding to each specific image. However, due to extensive personal images shared online, image-specific methods are limited by real-world practical applications. To address this issue, we are the first to investigate the creation of identity-specific cloaks (ID-Cloak) that safeguard all images belong to a specific identity. Specifically, we first model an identity subspace that preserves personal commonalities and learns diverse contexts to capture the image distribution to be protected. Then, we craft identity-specific cloaks with the proposed novel objective that encourages the cloak to guide the model away from its normal output within the subspace. Extensive experiments show that the generated universal cloak can effectively protect the images. We believe our method, along with the proposed identity-specific cloak setting, marks a notable advance in realistic privacy protection.