Not a private investigator.  Most likely a debt collector out of Seneca New York.  No address that I can find.  Ignore and block these calls.  How could a debt collector know anything about your social security number's status one way or the other?  This is an attempt to scare some money out of you.

Just because someone on the phone calling you says you owe a debt does not mean you actually owe it.

If a voice on the telephone claims you owe a debt:

1.    Demand the person give you his or her name, company name, and address
2.     Demand a debt validation letter by US mail.  E-mail no good.
3.    Do not pay  the collection agent or anyone else a  dime until the debt is validated

Of course they won’t do this, no scammer ever will, so simply ignore them and block their calls.

If they are bothering you, report them:

http://www.consumer.ftc.gov/articles/0149-debt-collection (Threatening civil proceedings with no intent to follow through, or threatening criminal process in order to collect a civil debt is a  violation of the Federal Fair Debt Collection Practices Act.)  The same goes for endless telephone harassment

Also contact your local attorney general

If they continue to bother you,  and you know you do not owe any money, tell them that you know this is  a debt scam and that you are making a complaint to the police for extortion.  Once you get a copy of the police report and they call you again , just read out the  file number and the name of the PD or Sheriff’s office involved.   Tell them you’ll be glad to send a copy to them at whatever address the jack***es are working out of now.

You'll probably have to yell at them and talk over them.
You have to get tuff with these people because,  being akin to thugs, brute force is (metaphorically speaking),  the only thing they understand.