We present a numerical study of the evolution of galaxy clustering when galaxies flow passively from high redshift, respecting the continuity equation throughout. While passive flow is a special case of galaxy evolution, it allows a well-defined study of galaxy ancestry and serves as an interesting limit to be compared to nonpassive cases. We use dissipationless N-body simulations, assign galaxies to massive halos at z = 1 and 2 using various halo occupation distribution (HOD) models, and trace these galaxy particles to lower redshift while conserving their number. We find that passive flow results in an asymptotic convergence at low redshift in the HOD and in galaxy clustering on scales above ~3 h⁻¹ Mpc for a wide range of initial HODs. As galaxies become less biased with respect to mass asymptotically with time, the HOD parameters evolve such that M₁/M_min decreases while α converges toward unity, where N_g(M) = exp (− M_min/M) [ 1 + (M/M₁)^α] . The satellite populations converge toward the Poisson distribution at low redshift. The convergence is robust for different number densities and is enhanced when galaxies evolve from higher redshift. We compare our results with the observed luminous red galaxy (LRG) sample from SDSS that has the same number density. We claim that if LRGs have experienced a strict passive flow, their N_g(M) should be close to a power law with an index of unity in halo mass. Discrepancies could be due to dry galaxy merging or new members arising between the initial and the final redshifts. The spatial distribution of passively flowing galaxies within halos appears on average more concentrated than the halo mass profile at low redshift. The evolution of bias for passively flowing galaxies is consistent with linear bias evolution on quasi-linear as well as large scales.