I'm thinking pre-"American dream" but I'd say any western, English-speaking country would have a reasonably similar dynamic.
Alright, so this question is equal parts history and economics. You didn’t specify a particular time period, so I’m not exactly sure what you mean by “before people could own their own homes.”
For the history component I can comment on medieval Europe. This is stereotypically a time when lords and knights controlled the majority of land and demanded rent from the serfs and freeholders residing on it.
Even at the height of medieval “feudalism” (a broad and debated term, but I’ll use it here), land ownership was never completely restricted to aristocrats.
Though many people were bound in serfdom to the land, a surprising number of peasantsowned land in a way that closely resembled land ownership today. Some of these peasants were particularly well-off commoners, who had bought or negotiated their freedom at some point in their family history.
Poorer landholders might be referred to as “cotters” or “cottagers.” These people were free in the sense that they owned land and few feudal obligations, but they often had to scrape a living by laboring for whoever would take them in. (In some sense the serfs had a bit more security)
These freeholders still owed “property taxes” to the local lord, but their obligations tended to be more flexible than that of serfs, especially as rent payments shifted from being paid with goods and services (days of labor, a cart of apples, etc) to being paid in the equivalent cash sum.
So what stopped medieval lords from raising their rents to whatever they liked? Put simply, custom and competition.
Much of the Middle Ages can be characterized by a process of developing “customs” between serfs and their lieges. There were strong cultural expectations as to what was acceptable for a lord to demand, and though they could certainly push the limits of, serfs could and would resist illegitimate demands.
Runaway serfs show up in court rolls fairly regularly, indicating that serfs often attempted to relocate to less demanding lords, and presumably succeeded fairly often.
The issue of a much larger issue after the Black Death, when labor was in massive shortage and landowners were desperate to attract labor to their idle fields.
This where economics come into play: offer lower rent, get more tenants.
Even though the landowning class was fairly exclusive throughout the Middle Ages, they were never able to form a cabal to raise rents, presumably because they were competing with each other for desirable tenants!
Serfs ran away despite laws restricting their movements, but a freeholder could buy and sell property more or less wherever they could afford. A freeholder facing particularly high rents would be well within his rights to sell off his land and move somewhere with more attractive rent scheme.
Serfdom as a social class was eroding rapidly by the high Middle Ages, so freeholders became a larger and larger economic force over the years.
If I can step away from the Middle Ages for a moment to make a general statement about economics…
Any investment with huge profit margins naturally attracts more investors. Those investors tend to raise the supply of available product, which almost always lowers the prices over time.
In the short term such agreements to artificially inflate rents may be possible, but the competition principle tends to undermine them over time.
Changing conditions, demographics and legal systems can all obscure and obstruct this process, but it is always there, chipping away at these sorts of agreements.
Hopefully this is at least partially answers your question!