Consequences of working with ITIN or fake Social after getting valid SSN

Since most DACA recipients are unable to update their Social Security numbers at their current place of work, they are continuing to work with whatever false information they provided to their employer when they first took that job.  This is clearly violation of what the United States government expects of immigrants who have been grant legal immigrant status of any kind.  Indeed, it is fact that SSN can almost never be changed and remains the same your whole life, the right path forward for anyone who used a phony number before is to start over.  This means that you may have to quit your current job and say goodbye to whatever other benefits you received from stealing an identity.  Continuing to use your ITIN or stolen SS# after you have received a genuine number is violation of the terms of agreement you agreed to when you applied for DACA.

Use of more than one Social Security number is a crime:  It is already known that it is technically impossible to file proper taxes if you have more than one identity (in other words, more than one identifying number like SSN) and by holding on to a fake number while having a real number is going to not only things very messy going forward, but you will still be breaking a series of United States fraud laws.  When the American government grants you a status in the country, it holds you to a much higher standard, expecting that you will have respect for US laws and you will follow them, and not ignore them just because your chances of being caught are minimal.  By not using your valid number, you are violating US laws but also causing financial self-harm.  Remember that the payroll taxes you are contributing to a fake SS# will never be given to you.  On the other hand if you work using your genuine identity, you will build a safety net.

Can you be caught?  Since the government is not actively pursuing this crime, unless you get into another legal trip, you will go scot-free, but this information can be found at the time of applying for permanent status or naturalization.  At the time of applying for US citizenship, it can be definitely used against you as it will be indicator that you are not a person with a good moral character.  That is why my recommendation will be to stop using your fraudulent identity immediately after a new number is received and start a fresh life with the new number.