I like your profile page too. One thing from your profile page, "neither reside nor work here lawfully", this may surprise you, but it is not against the law to rent housing to illegal immigrants. If it were against the law, and under penalty of property forfeiture, it would reverse and end the problem. These people couldn't survive among us without housing. Sure people could offer them jobs under the table, but without someplace to live, that money would be worthless.
What I mean is that their presence here is unlawful, regardless of whether they rent, share or buy housing.
Sadly, it does not surprise me at all that there are no penalties for renting to foreign trespassers. That is one little freedom of property rights that owners have. I know this because, starting in the early 1980s, I watched the area I grew up in transform from a quiet, clean, safe and sedate neighborhood into a raucous, filthy, crowded latin american ghetto. My mother remained, refusing to move because she was near her church. But they even threw rocks and broke the beautiful stained glass windows of the chapel.
Owners have the right to restrict the number of tenants per apartment, but apparently that is optional. Even restricting the number of tenants per unit would help. We never could figure out why that overcrowding was allowed. Aren't property owners supposed to care about property values?