[uxp]

It really depends on how the SSN is used, but using a false SSN is considered fraud.

If the party requesting it is using it for billing and collections, and you fail to pay a bill and they send it to collections, and subsequently report the collection to a credit agency, then it is a clear case of fraud. If you randomly happen to pick a valid SSN, then you are committing identity theft in addition to fraud.

If they are just using it as a Unique ID, they may not ever know that it's fake. None-the-less it is still fraud.