It is not possible because of the encryption that is legally required on the SSN field by the Federal Government.
When you do a search by SSN, we have to encrypt the SSN that you are searching for and compare that to the values in the table to look for a match. Without getting too deep into methods of encryption, it is not a simple substitution cypher. If it was, then a search might still be possible on a partial SSN, but such a cypher would be easy to crack through brute force decryption.