"someone's relative has a genuine item and lends it."
Yes this does happen. It gives credability to the notion of biometrics being a part of an ID. It is time to untie the bindings of this issue and a REAL ID would go far to do so.
I have a little experience with this issue on that note.
When I was young an Illegal Alien was using my SS#. This was never a problem until I filed my tax return. The IRS had no problem taking in cash until TWO sets of income were present.
Part of the problem is that the SS# is being used in ways it was not designed to be used. As a primary source of Identification. This is just another example of why we need a real ID.
You are right that the social security number is used differently these days. Also consider that if the income that is reported for the illegal is not included on the forms of the genuine owner, this is how the IRS finds people to ding. But that information cannot be shared with INS.
It affects the genuine taxpayer, and is even more destructive to the retiree, who is then barred from withdrawing benefits and is taxed until he or she can prove the fraud (there is a story of a woman who is retired and has to fix this every year).
There is also the problem of credit card fraud.
Guard your information as carefully as possible.