As of August 1999, there were nearly 62 million individuals in the database. If the person's death was reported and recorded, information is VERY accessible. This database is made available to the public through sales to private suppliers. The database is updated quarterly, but the suppliers may or may not upgrade that frequently. You should always check the effectivity for the database you are using.
Some suppliers even offer the database online using their own search engines.
Once you have located the database, use the indicated search options for that source. The FamilySearch program does not allow you to search by Social Security number, but many of the commercial versions do. The first part of the Social Security number is a code indicating the state of issuance. This can be a good clue for a place of residence. For example, my Social Security number was issued in Kansas - since I wasn't born, baptized, or married there, and didn't go to college there, one should guess that perhaps I lived there at some point, probably before going to college.