One of the major reasons that our cities become expensive in our "modern" society is that we don't have land value taxes. If we have a land value tax, then when someone decides they can't afford to keep paying the tax, they sell it to someone who can OR they find a way to make the things built on that property much more valuable so that the tax is affordable. It provides a very strong incentive for property owners to do things like tearing down single family homes and building multi-unit condos in their place. Because there are multiple units where there was previously only one, the cost of living actually goes down. This is why it's considered a very beneficial tax: it promotes efficient use of land from economic perspectives. (This also applies to businesses: if a business isn't able to afford the land value tax for their property, they have strong incentives to find a way to make the use of their land more valuable or to sell it to someone who can. And if the value of their land is going up more than they can afford, that implies that there likely are potential buyers who could make better use of it.)
For us to go from where we currently are to a land value tax would require a transition period, because it takes time to tear things down and build new things. But a society that was implementing a land value tax would see new properties opening up like I described above on a regular basis. So if you couldn't afford the land value tax, you would still be able to stay in the same city (and probably more cheaply and in a nicer, newer condo) unless you absolutely required a single family home or similar low-density housing.