(They remember it, or they write it down and store it with their other valuable pieces of paper.)
In practice, by just marking the damn pages.
Edit: latest statistics show >95% have BankId on a smartphone. See https://www.bankid.com/assets/bankid/stats/2019/statistik-20...
A super high end hotel in Singapore would leave client bookings at the check in counter with address, name, credit card also.
You can go to a bank, say "hi im John, my social is 123456789, I'd like to take a ten thousand dollar loan" and they'll give it to you if their records show that the name belongs to that number.
If that's so, why isn't this happening in massive numbers, given for example the 143 million SSNs that leaked through equifax?
I think it's harder these days than the other poster says, but there is still plenty of financial fraud.
When I had my identity stolen the crooks still had some Fake ID with my name and info. They found small cellphone kiosks (a makeshift promotional tent) inside large stores with lax security to make their purchases.