Context. Group environments are thought to play a key role in shaping galaxy evolution prior to cluster accretion. However, direct observational evidence linking group─cluster interactions to the transformation of low-mass galaxies remains scarce. Aims. The nature and origin of the W cloud, located in the southern outskirts of the Virgo cluster, have been reexamined in order to better understand the dynamical processes driving group accretion and galaxy transformation during cluster assembly. Methods. A comprehensive analysis combining the spatial distribution, kinematics, and stellar population properties of galaxies in the W cloud and its surroundings reveals the dynamical structure of this system. This multidimensional approach allows us to characterize the three-dimensional structure of the system, assess its dynamical state, and identify the dominant environmental mechanisms at work. Results. We conclude that the W cloud is not a filament of the large-scale structure seen in projection. Instead, the W cloud is dominated by a compact galaxy group (the W group) currently interacting with the main cluster. Moreover, a newly discovered, dynamically coherent tail of galaxies (the W tail) connects the W group to the cluster and exhibits a continuous sequence in velocity, velocity dispersion, and three-dimensional distance. The low-velocity component of the tail is already gravitationally bound to Virgo, while higher-velocity galaxies remain dynamically connected to the group and are still infalling. The W tail forms a planar structure aligned with the orbital geometry of the W group, strongly indicating a tidal origin. The stellar mass and color properties of their members show that the stripped population is dominated by low-mass, star-forming dwarfs that remain in the blue cloud, with their slightly bluer colors relative to the W group naturally explained by their lower stellar masses rather than by environmentally induced star formation enhancements. Conclusions. The W group─W tail system provides a well-resolved example of an active group─cluster interaction, illustrating how low-density galaxy groups can deliver largely unprocessed dwarf galaxies into clusters. This system offers key observational constraints on the hierarchical assembly of galaxy clusters and the buildup of their dwarf galaxy populations.