I assume it's a scam

Got a call at home today from "Rachel Riley," who asked for me by name. She did not identify what organization she was supposedly representing. Once I confirmed my name she asked for the last 4 digits of my Social Security number "for verification." I said I wasn't giving her any information when I didn't know who she was. Sounding a little hurt she repeated that she was "Rachel Riley."

"Yes, but why are you calling me?"
"I'm calling about some personal business of yours."
"What personal business would that be?"
"I can't discuss it until I verify your identity. But it's something that I'm sure you want to clear up."

At this point I hung up. It seems obvious that it's some kind of scam, but what exactly was she after? The last 4 digits of a SSN are not really good for much. Could it be someone that has obtained my full SSN and was trying to verify that they had the right one before doing something nefarious with it?

Has anyone else gotten a call like this recently?