To request a new social security card online, it takes your credit report information.

Thanks, Equifax data breach.

Good news: the SSA will only send your new card to your current address as reported in your credit report.

Thanks, USPS.

So, in summary, sounds like getting someone else’s social security card is pretty easy. Admittedly there’ll be a nifty paper trail, but I’m sure that’s solvable too.