We present a numerical study of the evolution of galaxy clustering whengalaxies flow passively from high redshift, respecting the continuityequation throughout. While passive flow is a special case of galaxyevolution, it allows a well-defined study of galaxy ancestry and servesas an interesting limit to be compared to nonpassive cases. We usedissipationless N-body simulations, assign galaxies to massive halos atz=1 and 2 using various halo occupation distribution (HOD) models, andtrace these galaxy particles to lower redshift while conserving theirnumber. We find that passive flow results in an asymptotic convergenceat low redshift in the HOD and in galaxy clustering on scales above ~3h-1 Mpc for a wide range of initial HODs. As galaxies becomeless biased with respect to mass asymptotically with time, the HODparameters evolve such that M1/Mmin decreaseswhile α converges toward unity, whereg(M)>=exp(-Mmin/M)[1+(M/M1)α].The satellite populations converge toward the Poisson distribution atlow redshift. The convergence is robust for different number densitiesand is enhanced when galaxies evolve from higher redshift. We compareour results with the observed luminous red galaxy (LRG) sample from SDSSthat has the same number density. We claim that if LRGs have experienceda strict passive flow, their g(M)> should be close toa power law with an index of unity in halo mass. Discrepancies could bedue to dry galaxy merging or new members arising between the initial andthe final redshifts. The spatial distribution of passively flowinggalaxies within halos appears on average more concentrated than the halomass profile at low redshift. The evolution of bias for passivelyflowing galaxies is consistent with linear bias evolution onquasi-linear as well as large scales.