The counterintuitive phenomenon of negative linear compressibility (NLC) has tremendous application potential in the design of ultrasensitive pressure sensors, artificial muscles, and actuators. However, materials with this uncommon mechanical behavior usually suffer from a narrow operating pressure range or frequently undergo sudden structural collapse. Here, we report the sustainable negative compressibility of stable A-site-free perovskite titanium oxyfluoride (TiOF₂) along its c-axis over a very broad pressure range. The persistent NLC of this open-framework structure is ascribed to the anisotropic distortion of constituent octahedra, a result of the gradual volume reduction via flexible polyhedral tilting. Moreover, the NLC axis varies almost linearly with the optical band gap, promoting its applications in high-precision devices. This work paves a way to exploit the negative compressibility effect for designing versatile materials with enhanced mechanical performance.