As an example, in the UK, social security provided a formula that determined the "permissible rent".

If I claimed housing benefit, they would look at the formula, and tell me "Your housing benefit is a maximum of £x: if your rent is more than that, you have to pay it out of your own pocket".

The formula dictated the maximum rent for state-subsidised housing: almost no tenant claiming social security could afford to pay above the subsidised amount from their own pocket.

However, the formula accounted for rental prices in the region over the previous few years, and effectively acted as a price escalator. All DSS landlords priced their rent at the maximum permitted, and the subsidy therefore regularly increased with their prices. As a result, buy-to-let became very popular, with a number of training courses/presentations pitching this price-escalation practice, which also helped sustain the price escalation.

As rental prices increased for state-subsidised landlords, unsubsidised private tenants also had their rents increased, both sectors mirroring each other.

The government have since introduced caps to various benefits, which may put a stop to the routine escalation, but it's a good demonstration of some of the legislative flaws. For most people, a place to live is high if not top on their priorities, and most debt advice councilors recommend paying rent/mortgage as the top priority, above every other bill, so even given excruciating increases, most people will still pay it.

Because not everyone is poor yet, and rent is among the last things you can save on.

As a native of England and not an economics professor I feel here it's because it's the only alternative to buying (many can't buy) and there's still a juicy percentage of combined monthly wages /not/ spent on rent up for grabs. The market is bearing the increases by not saving, reducing food spend, etc.