Context. The fine structures of the solar chromosphere, driven by photospheric motions, play a crucial role in the dynamics of solar magnetic fields. Many such structures have already been identified, such as fibrils, filament feet, and arch filament systems. Nevertheless, high-resolution observations show a wealth of structures whose nature remains elusive. Aims. We observed a puzzling, unprecedented chromospheric fibril singularity in the close vicinity of a blow-out solar jet and a flaring loop. We aim to understand the magnetic nature of this singularity and the cause of its activity using coordinated high-resolution, multi-wavelength observations. Methods. We aligned datasets from Solar Orbiter, SST, IRIS, and SDO. We re-projected the Solar Orbiter datasets to match the perspective of the Earth-based instruments and performed potential field extrapolations from Solar Orbiter/PHI data. We analysed the spatial and temporal evolution of the plasma structures and their link with the surface magnetic field. This led us to derive a model and scenario for the observed structures, which we explain in a general schematic representation. Results. We have discovered a new feature: a singularity in the chromospheric fibril pattern. It forms in a weak magnetic-field corridor between two flux concentrations of equal sign, at the base of a vertically inverted-Y-shaped field-line pattern. In this specific case, some activity develops along the structure: first, a flaring loop at one end, and second, a blow-out jet at the other end, where a coronal null point was present and associated with a chromospheric saddle point located on the fibril singularity. The observations suggest that both active phenomena are initiated by converging photospheric moat flows that exert pressure on this fibril singularity.