People who are crossing the border illegally are never going to come close to qualifying for a mortgage, at least in next 5-10 years.

But a different kind of immigration does affect the crisis, and it is on the other end. You can fast track permanent residency by investing money, around $1m, into a US business. So every corrupt technocrats, police and army higher ups, politicians, gang leaders, unscrupulous business people I know of from my native developing country own multiple houses for themselves, their spouses and kids in US and Canada. This is what is making homeownership more and more unaffordable for average Americans.

From 2007 to 2019 the estimated number of unauthorized immigrants was slightly declining[1], at the same time that the population of the US as a whole (and the housing shortage) was growing, so it certainly wasn't a significant part of the problem then. From 1990 to 2007, the unauthorized migrant population grew about 500k/year relative to about 3M/year total. Even unauthorized migrants accounted for 17% of the population like they did then, which is debatable, that still wouldn't account for all of the discrepancy between housing growth and population growth. So it is fair to ask for numbers that actually support the parents position.

[1] https://www.pewresearch.org/short-reads/2023/11/16/what-we-k...