This is pretty basic math. Just think about Monopoly (yes, the board game).
Housing is a finite resource. You can buy it or you can rent it. When you buy, you build equity. When you rent, it's pure expenditure.
So what happens when nobody can buy? They are forced to rent. Demand for rentals rises, which allows landlords to raise their rents.
So how does someone with very deep pockets turn this to their advantage?
First, starting one metropolitan area at a time, you buy up everything you can. If you coordinate with other investors, all the better. The goal is to strangle supply for buyers and prevent anyone who can't pay cash upfront from making a purchase. When people are unable to buy, they are forced to rent. So for buyers supply is down and costs are WAY up, and being locked out of buying means demand is up for rentals.
Now, renters also aren't building equity; when means it is perpetually more difficult for them to buy in the future as long as they kept away from that equity-building opportunity.
So as an "investor" you can now have a lot of different levers for manipulating both the supply and demand sides of the housing market. For example... what happens if you have more rental property than people willing to pay your asking price? Won't you be forced to lower your prices? First of all, that rarely happens - because as an investor, you target places that already have reliable, consistent demand (e.g. big cities and metropolitan areas). If you have to occasionally let a property go unoccupied for a few months, it's still no biggie... you keep those prices high and do not, under any circumstances, devalue the market (for your own sake as well as your investment cronies). Now, if there were competition, prices might be driven down... so how do you avoid competition? You collude. But that's illegal... so to avoid accusations of collusion and price fixing, you farm out your rates to a third party service that all your cronies also use: RealPage. It's not collusion or price fixing if you use a middleman. So now you are making bank on rental rates that will see a full return on your (higher than the properties value) investment in 15 years or less.
This has been going on for well over a decade, and these "investors" are now printing money on some of their earliest purchases, with no intention of EVER putting anything back on the market.
TL;DR; Buy all the supply, force plebes to rent, control the prices, profit. Just like Monopoly.