The neutral atomic gas content of galaxies is usually studied in the H I 21 cm emission line of hydrogen. However, as we go to higher redshifts, owing to the weak strength of the transition, we need very deep integrations to detect H I emission. The H I absorption does not suffer from this dependence on distance as long as there is a sufficiently bright radio source to provide the background continuum. However, resolved H I absorption studies of galaxies are rare. We report one such rare study of resolved H I absorption against the radio galaxy 3C 433 at z = 0.101, detected with the Very Large Array. The absorption was known from single-dish observations, but owing to the higher spatial resolution of our data, we find that the absorber is located against the southern lobe of the radio galaxy. The resolved kinematics shows that the absorber has regular kinematics with an H I mass ≲3.4 × 108 M⊙ for Tspin = 100 K. We also present deep optical continuum observations and Hα observations from the Gran Telescopio CANARIAS (GTC), which reveal that the absorber is likely to be a faint disc galaxy in the same environment as 3C 433, with a stellar mass of ∼1010 M⊙ and a star-formation rate of 0.15 M⊙ yr−1 or less. Considering its H I mass, H I column density, stellar mass, and star-formation rate, this galaxy lies well below the main sequence of star forming galaxies. Its H I mass is lower than the galaxies studied in H I emission at z ∼ 0.1. Our GTC imaging has revealed, furthermore, interesting alignments between Hα and radio synchrotron emission in the H I companion and in the host galaxy of the active galactic nucleus as well as in the circumgalactic medium in between. This suggests that the shock ionization of gas by the propagating radio source may happen across a scale spanning many tens of kpc. Overall, our work supports the potential of studying the H I content in galaxies via absorption in the case of a fortuitous alignment with an extended radio continuum source. This approach may allow us to trace galaxies with low H I masses which would otherwise be missed by deep H I emission surveys. In conjunction with the deep all-sky optical surveys, the current and forthcoming blind H I surveys with the Square Kilometre Array (SKA) pathfinder facilities will be able to detect many such systems, though they may not be able to resolve the H I absorption spatially. Phase 1 of the SKA, with its sub-arcsecond resolution and high sensitivity, will be all the more able to resolve the absorption in such systems.