This paper presents a theoretical investigation of the polarization and magnetic sensitivity of the near-ultraviolet (near-UV) solar spectral lines of Fe II between 250 and 278 nm. In recent years, UV spectropolarimetry has become key to uncovering the magnetism of the upper layers of the solar chromosphere. The unprecedented data obtained by the CLASP2 suborbital space experiment across the Mg II h and k lines around 280 nm are a clear example of the capabilities of near-UV spectropolarimetry for magnetic field diagnostics throughout the whole solar chromosphere. Recent works have pointed out the possible complementary diagnostic potential of the many Fe II lines in the unexplored spectral region between 250 and 278 nm, but no quantitative analysis of the polarization and magnetic sensitivity of those spectral lines has been carried out yet. To study the polarization signals in these spectral lines, we create a comprehensive atomic model including all the atomic transitions resulting in strong spectral lines. We then study the magnetic sensitivity of the linear and circular polarization profiles in a semiempirical model representative of the quiet Sun. We present a selection of Fe II spectral lines with significant linear and circular polarization signals and evaluate their diagnostic capabilities by studying their formation heights and magnetic sensitivity through the action of the Hanle and Zeeman effects. We conclude that when combined with the CLASP2 spectral region these Fe II lines are of interest for the inference of magnetic fields throughout the solar chromosphere, up to near the base of the corona.