If an illegal alien works with a fake Social Security number the employer is notified.
If that employer continues the employment he has violated a federal law and should be fined or jailed
https://www.law.cornell.edu/uscode/text/8/1324a (long read).
Refugees should be able to use the "resources" of their host country for a reasonable length if time. The condition of residency of an ordinary immigrant should be limited to the "resources" of public schools, adult education and public health services as needed.
You are just being fed a line of shit and buying it hook line and sinker. All whine and no solutions.
Change the laws if necessary to the above ends.
See the first few pages -- elgibility
https://fas.org/sgp/crs/misc/RL33809.pdf
Noncitizen Eligibility for Federal Public
Assistance: Policy Overview
Alison Siskin
Specialist in Immigration Policy
December 12, 2016
Noncitizen Eligibility for Federal Public
Assistance: Policy Overview
Alison Siskin
Specialist in Immigration Policy
December 12, 2016
Congressional Research Service
7-5700
www.crs.gov