The original Fuzzy Vault scheme is inherently restricted to codes based on polynomial evaluations, in particular Reed–Solomon codes. This structural dependency limits its applicability to a narrow class of error-correcting codes and constrains possible generalizations. In this work, we reformulate the scheme within the framework of generic linear codes, detaching the construction from its polynomial structure. We define locking and unlocking procedures compatible with any linear code that meets a set of explicit conditions, which we identify and justify. This reformulation makes it possible to explore the use of alternative codes that satisfy these conditions, and we detail how Reed–Solomon codes fit into this framework. It also clarifies the internal organization of the scheme and its compatibility with different code families. In addition, we propose a method for embedding the protected secret inside the vault structure, thereby removing the need for external storage and ensuring that all recovery elements remain encapsulated within the scheme itself. In this variant, the error vector contains values obtained by applying a cryptographically secure one-way function to a randomly chosen secret, making them indistinguishable from random noise.