So here's my experience recently
We applied rental apartment online for the apartment that we really like, couple days later, leasing office called us that our information isn't enough,
they asked for my legal status which is weird because it didn't happen at my current rental apartment.
So I emailed copy of my expired green card and 18 months extension letter. But it's not over yet
Leasing office contacted me said "yea...the letter says you can work and travel, doesn't says you are legal living in the U.S. "
I was very speechless about this argument, so I explained I can use the letter come back to the U.S., and I'm just trying to apply an apartment here.
then she said "Your SSN is for working only, we need to see the card to verify the information."
wow...I have been used the card since graduated from school, never had any issues.
I was planning to update it after I'm citizen, didn't think it could be the issue now.
I'm just share this experience to let people know this could happen
and probably should update SSN information after you get the green card.
Also I looked into laws that only CA and NY can't ask tenant's legal status.