  Controllable Rydberg atom arrays have provided new insights into fundamental
properties of quantum matter both in and out of equilibrium. In this work, we
study the effect of experimentally relevant positional disorder on Rydberg
atoms trapped in a 2D square lattice under anti-blockade (facilitation)
conditions. We show that the facilitation conditions lead the connectivity
graph of a particular subspace of the full Hilbert space to form a 2D Lieb
lattice, which features a singular flat band. Remarkably, we find three
distinct regimes as the disorder strength is varied: a critical regime, a
delocalized but nonergodic regime, and a regime with a disorder-induced flat
band. The critical regime's existence depends crucially upon the singular flat
band in our model, and is absent in any 1D array or ladder system. We propose
to use quench dynamics to probe the three different regimes experimentally.
