Even if you gave a fake SSN to, say, a landlord (they need it to run a background and credit check on you and to better chase you down if you don't pay your rent) that would almost certainly be considered either fraud or theft by deception.

Generally, you provide the entity your SSN because they have a legitimate need to identity you, and that includes identifying you as you outside their internal system.

https://www.ssa.gov/employer/stateweb.htm

That leaves you with six digits to choose.

Secondly, that wouldn't work, the insurance company already knows your SSN. If your insurance is provided through your employer your employer already gave it to your insurance company when they set up your benefits. You need to give your employer your real SSN to pay taxes. If your insurance is provided through the government (medicaid, medicare, tricare) then the government already knows your SSN. You BEST not be giving the government a fake SSN to collect benefits, that's all sorts of illegal.

>Secondly, that wouldn't work, the insurance company already knows your SSN

It could totally work, it’s really easy to get a card open with another SSN and then accurint or whatever the insurance company uses will just return multiple SSNs.

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.