It is very common among undocumented immigrants to use stolen Social Security numbers that they buy from criminals. It is also somewhat common for many immigrants to use the details of a legal family member or friend. Needless to add, the largest SS# are simply numbers that don't seem to belong to anyone and are randomly generated by criminals who are in the business of printing fraudulent Social Security cards for a price. While many undocumented aliens do not realize that they are breaking any laws by doing so or hurting anyone else, the reality is that not only many laws are being broken, in some cases, real financial harm is being done to legal residents, particularly children (criminals target children when committing identity theft). Many victims are then unable to find a job or use banking/credit services because of the suspicious activity on their number.
In order to discourage identity theft and abuse of SSN, the USCIS will make it harder for you to find work by using someone else's SSN (it already is impossible to get an eVerify approval with a fake number). Going forward, the algorithm of eVerify will be able to detect if a person is using another person's totally valid number. If your employer finds that out (for undocumented aliens the safe assumption to make is that the employer is using eVerify despite widespread reports that many employers do not), it will be clear to them that you are breaking the law and will most likely result in withdrawal of the job offer. It is also likely that law enforcement may be alerted as a potential case of identity theft.
What to do if you are a valid owner of that Social Security number? If that happens to you, in many ways it is good because you now know that your number has been compromised. You will essentially be given a “Tentative Nonconfirmation” (TNC) by your employer and while it will require a trip to the local Social Security office (not a fun thing to do for anyone of us due to the lines and bored bureaucrats who work there), you will be able to get an approval after providing evidence of your legal status, which for a citizen can be a birth certificate or naturalization certificate or passport and for permanent residents and legal residents it can be their passport and an evidence of a visa or approval of some kind from the USCIS. At that point, the USCIS and SSA will be alerted that other unauthorized users have been using your number and you will be protected from identity theft.