ironman, it isn’t just renters. When you sell a home, usually your SSN in on the docs that is available to the buyer (don’t remember if it’s the other way around too).

Nevertheless, the best way to protect yourself if to get a credit freeze and/or subscribe to credit monitoring.

Trust me, your SSN is mishandled much more than you are aware of it, making this one particular situation minute compared to everything else. I’ve had cases which background check agencies were emailing my ssn in the subject field between me at my yahoo account,etc.