The unusually low velocity dispersion and large sizes of `feeble giant' galaxies, such as Crater II or Antlia II, pose a challenge to our understanding of dwarf galaxies in the Lambda Cold Dark Matter (LCDM) cosmogony. Their low velocity dispersions suggest either a dark halo mass much lower than the minimum expected from hydrogen cooling limit arguments, or one that is in the late stages of extreme tidal stripping. The tidal interpretation has been favoured in recent work and is supported by the small pericentric distances consistent with available kinematic estimates from Gaia. We use N-body simulations to examine this interpretation in detail, assuming a Navarro-Frenk-White (NFW) profile for the Crater II and Antlia II progenitor halos. Our main finding is that, although the low velocity dispersions can indeed result from the effect of tides, the large sizes of feeble giants are inconsistent with this hypothesis. This is because galaxies stripped in mass to match the observed velocity dispersions are also reduced to sizes much smaller than the observed half-light radii of Crater II and Antlia II. Unless their sizes has been substantially overestimated, reconciling systems like these (including Andromeda XXV and XIX) with LCDM requires that either (i) they are not bound and near equilibrium (unlikely, given their crossing times are shorter than the time elapsed since pericentre), or that (ii) their progenitor halos deviate from the assumed NFW profile. The latter alternative may signal that baryons can affect the inner halo cusp even in extremely faint dwarfs or, more intriguingly, may signal effects associated with the intimate nature of the dark matter, such as finite self-interactions, or other such deviations from the canonical LCDM paradigm.
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