Social Security numbers can never be changed

Almost.  Except for very small number of extremely rare instances (identity theft, violence against women, etc.) in which the Social Security Administration will issue a new number to an individual (the process is very convoluted and requires a lot of paperwork and coordination with the SSA).  In any case, even after that to straighten out everything with the IRS, credit rating agencies, and anyone else interested in your SSN is frustrating and problematic.

The reason I point this out is that I have been receiving emails from DACA approved DREAMers who have valid SS# now arguing that one can change a Social Security number whenever they want, or that one is allowed to do so ten times in one's life, or that all one needs to do is to change the IRS W4 form.

None of this is true.  If you are a DREAMer who worked illegally with a fake SSN or you stole someone's identity and now have a valid for employment SS#, legally speaking you simply cannot change your number anywhere.  Those immigrants who had an ITIN but used it to work illegally maybe able to switch it to a valid SSN (that too may come to bite you later because it will confirm and create a paper trail of working without authorization) but there is no provision or procedure to simply change your SSN.



Having said that, we are all aware that there are employers who knowingly employ unauthorized immigrants and either they are kept off the books or they mess with their records and what they tell the IRS and SSA.  Maybe they can accommodate your request to change your Social Security number by, yet again, manipulating their records (basically they will fire you with your old false SSN and then hire you with your new valid SSN), but that would be breaking US law and they maybe subject to prosecution.

Finally, the only hope that DREAMers in this situation have is to start a clean life after they are approved by USCIS and issued a new valid for work SSN by SSA.  Doing anything else will make your case even murkier and can put you in trouble later on.