However lets say it does, many illegal immigrants have multiple people in their home.

Immigrants in lower income, in particular, can be very respectful and dependable renters if you screen them right.

Lots of good people out there that don't qualify for conventional mortgages that would treat the property better and fix it up, specially immigrants like myself.

Our 4 tenants are immigrants and English is not their first language.We did not want to continue to pick up the rent for many reasons.We opened an account at a Bankm with a branch  very near them and asked them to bring their rent to the bank on the  1st of every month.  

I have also started actively working with the various immigrant communities here which (aside from some language barriers) has gone well so far, but takes a little flexibility and extra attempts at cultural understanding at times. 

A few years ago I approved a couple who were "rejected" by SmartMove because they were recent immigrants, and the app had difficulty verifying their identities.

You don't need this at all because if the police or immigration/DHS come asking you have to give them information anyhow.

Immigration status is not a factor.There are many lawful reasons why a person may reside in the U.S. and may not be eligible for either a SSN or ITIN.

Art students are also flaky, even graduate students.Some groups of people were a little more challenging, like immigrants who didn't understand American landlord-tenant relationships at first, or tenants who weren't fluent in English (my only fluent language) so they might need a bit more of my time, but maybe never otherwise caused major problems.You just can get a bad/good tenant from any tenant base, really. 

He has no income and he cannot return here due to immigration changes.