We use deep optical photometry from the Next Generation Virgo Cluster Survey [NGVS] to investigate the color-magnitude diagram for the galaxies inhabiting the core of this cluster. The sensitivity of the NGVS imaging allows us to continuously probe galaxy colors over a factor of ∼ 2×10 5 in luminosity, from brightest cluster galaxies to scales overlapping classical satellites of the Milky Way [M g ∼ -9; M * ∼ 10 6 M ], within a single environment. Remarkably, we find the first evidence that the RS flattens in all colors at the faint-magnitude end [starting between -14 ≤ M g ≤ -13, around M * ∼ 4 × 10 7 M ], with the slope decreasing to ∼60% or less of its value at brighter magnitudes. This could indicate that the stellar populations of faint dwarfs in Virgo's core share similar characteristics [e.g. constant mean age] over ∼3 mags in luminosity, suggesting that these galaxies were quenched coevally, likely via pre-processing in smaller hosts. We also compare our results to galaxy formation models, finding that the RS in model clusters have slopes at intermediate magnitudes that are too shallow, and in the case of semi-analytic models, do not reproduce the flattening seen at both extremes [bright/faint] of the Virgo RS. Deficiencies in the chemical evolution of model galaxies likely contribute to the model-data discrepancies at all masses, while overly efficient quenching may also be a factor at dwarf scales. Deep UV and near-IR photometry are required to unambiguously diagnose the cause of the faint-end flattening.