Insurance companies may request it for verification of the identity of patient.
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.