This person could have been an illegal, but there is a non-zero chance you just both had the same one. It does happen, or at least did.
Sidenote: I don't bear any ill will towards whoever used my SSN. It's not like I was targeted, or even that any harm to me was intended. This was a "hack" of a dysfunctional immigration and employment system, in a way that's totally obvious and easy to anticipate. My ire is reserved for those in positions of responsibility who maintain a regime that is manifestly not fit for purpose.