We investigate the effects of an early cosmological period, dominated by primordial 2-2-holes, on axion dark matter. 2-2-holes emerge in quadratic gravity, a candidate theory of quantum gravity, as a new family of classical solutions for ultracompact matter distributions. These objects have a black hole exterior without an event horizon and hence, as a probable endpoint of gravitational collapse, they do not suffer from the information loss problem. Thermal 2-2-holes exhibit Hawking-like classical radiation and satisfy the entropy-area law. Moreover, these objects, unlike BHs, have a minimum allowed mass and hence naturally give rise to stable remnants. In this paper, we consider the remnant contribution to dark matter (DM) small and adopt the axion DM scenario by the misalignment mechanism. We show that a 2-2-hole domination phase in the evolution of the universe changes the axion mass window from the dark matter abundance constraints. The biggest effect occurs when the remnants have the Planck mass, which is the case for a strongly coupled quantum gravity. The change in abundance constraints for the Planck mass 2-2-hole remnants amounts to that of the Primordial Black Hole (PBH) counterpart. Therefore; since we use the revised constraints on the initial fraction of 2-2-holes from GWs, the results here can also be considered as the updated version of the PBH case. As a result, the lower limit on the axion mass is found as m a ∼ 10 −9 eV. Furthermore, the domination scenario itself constrains the remnant mass M min considerably. Given that we focus on the pre-BBN domination scenario in order not to interfere with BBN (Big Bang Nucleosynthesis) constraints, the remnant mass window becomes m Pl ≲ M min ≲ 0.1 g.