Here's how two economists describe the filtering process:
The filtering model describes the housing market as a series of submarkets differentiated by unit quality. Rents fall as quality declines, so units that are lower on the quality ladder have lower rents than units of the same size in the same location at the top. Without expenditures on maintenance, renovation, and repairs, units decline in quality as they depreciate physically and technologically. As this occurs, the units move down the quality ladder. The cost to maintain a given level of quality is assumed to increase with unit age. Extra expenditures on maintenance and renovation can move units back up the ladder. Relative rents in the different submarkets vary with the distribution of income across households (demand) and the supply of units in that submarket. When quality is least expensive to provide at the time units are built, new units will be of high quality. The supply of the most affordable, lowest quality units will be those units built in earlier periods that have been allowed to depreciate and move down-to filter down-the quality ladder. Landlords will choose a level of maintenance to maximize profits, and that choice determines into which housing submarket their unit will fall. When incomes, population, and the housing stock raise rents in the submarket for higher quality units relative to those in the submarket for lower quality units, landlords in the latter submarket have a greater incentive to increase maintenance, renovation, and repair expenditures to cause units to filter up, that is, to move to the higher quality submarket. Reducing the supply of low-end affordable units can potentially exacerbate affordability problems for the least well-off.
That's from Somerville and Mayer, Government Regulation and Changes in the Affordable Housing Stock (pdf). Filtering is a tested, empirically-validated model. It is how housing markets work.