The Texas research is consistent with the finding that crime along the Mexican border is much lower than in the rest of the country, homicide rates in Mexican states bordering the United States are not correlated with homicide rates here, El Paso’s border fence did not lower crime, Texas criminal conviction rates remain low (but not as low) when recidivism is factored in, and that police clearance rates are not lower in states with many illegal immigrants – which means that they don’t escape conviction by leaving the country after committing crimes.
https://www.cato.org/blog/illegal-immigrants-crime-assessing-evidence