You should have been told you were hired before handing over your social security card. The only time they should be collecting your Social Security card is if they are making a copy for I9 verification. That is only done if they offer you a job. If you are wondering if you got the job and they aleready have copies of your personal information, you may want to give them a call.

Is this with a reputable company in your area?

Yes, at a group hiring event in which I was hired. All documents had to be presented ( signed application, ID, resume, and SSN card).