Answer: Be honest, report illegals to the Federal Govt... 
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"BUILDING A WALL" BETWEEN THE US'S SOUTHERN STATES & MEXICO IS NOT REQUIRED to appropriately & ethically remediate the country's egregious illegal trespassing-by-foreigners problems... 

All that is needed is the passing of several new laws by the US's Congress that would:

A) mandate the implementation of a federally-funded national identity card system... 

One that would result in ALL persons residing in the country legally (that are over 10-years of age) being issued high-technology photo ID (by the federal govt), & required to have such on their person at all times when in public spaces;

B) make it a criminal offence** for ALL employers, contractors, health care providers & educational facilities if they do not: 

-  ascertain the residency status of ALL persons hired by/contracted with & or that are provided services; 

and  

- report all illegal trespassers (persons in the US illegally) to Federal Authorities;