"Something puzzles me. If we have a glut of empty unsold houses, where did the people go?"
In theory your trepidation is correct, but as a practical matter, the same laugh a minute banks that brought you that glut in the single family dwelling market also financed boat loads of apartments and condos, and got Fannie Mae to declare $3000/month per apartment houses classed as low income housing and therefore could buy the paper and sell a tranche to you.
As a practical matter the monthly expected rent of the apartment or monthly payment on the condo was taken as a derivative of the debt service amounts of residential houses.
So, if you look at the amount of people who want to buy a house with the amount of housing available there is no "glut".
This same test, of course is true of Ferrari's and yachts until the real price is considered. On the other hand if the government will pay the monthlies, then there will be a line for Ferrari's.