The inner kiloparsec regions surrounding sub-Eddington (luminosity less than 10-3 in Eddington units, L Edd) supermassive black holes (BHs) often show a characteristic network of dust filaments that terminate in a nuclear spiral in the central parsecs. Here we study the role and fate of these filaments in one of the least accreting BHs known, M31 (10-7 L Edd) using hydrodynamical simulations. The evolution of a streamer of gas particles moving under the barred potential of M31 is followed from kiloparsec distance to the central parsecs. After an exploratory study of initial conditions, a compelling fit to the observed dust/ionized gas morphologies and line-of-sight velocities in the inner hundreds of parsecs is produced. After several million years of streamer evolution, during which friction, thermal dissipation, and self-collisions have taken place, the gas settles into a disk tens of parsecs wide. This is fed by numerous filaments that arise from an outer circumnuclear ring and spiral toward the center. The final configuration is tightly constrained by a critical input mass in the streamer of several 103 M ☉ (at an injection rate of 10-4 ${M}_{\odot }\,{{\rm{yr}}}^{-1}$ ); values above or below this lead to filament fragmentation or dispersion respectively, which are not observed. The creation of a hot gas atmosphere in the region of ~106 K is key to the development of a nuclear spiral during the simulation. The final inflow rate at 1 pc from the center is ~1.7 × 10-7 M ☉ yr-1, consistent with the quiescent state of the M31 BH.