One has got nothing to do with the other. Illegal immigrants aren’t driving up housing costs. Standard of living is stagnant, because wealth doesn’t “trickle down” like Reagan promised us. It trickles up. You’re repeating right wing talking points.
The "demand" in supply and demand means "how much money are people able&willing to invest into x"
For illegal immigrants, the answer to that is "not a lot"
I assure you, they have enough money to rent a home or apartment. Most are not homeless. To say even 1% of illegal immigrants are homeless a year after arriving would be a stretch.