Not seen in this inflammatory take:
First:
Police would be contacted any time a failed background check happens. Volunteering and failing a background check is not illegal. Perusing a person based on a failed background check is presumption of guilt.
Now if they lie about details to try and pass the background check, that's when it's illegal and should be reported to authorities, regardless of migrant, citizen, etc.
Second:
Unlawful possession of a firearm is a matter for police only, which ICE is not. Nor is it under their jurisdiction to handle illegally obtained weapons. They would have to turn right around and call the police anyway. (See
8 U.S. Code § 1357 - Powers of immigration officers and employees)
Third:
There's a growing movement by both Democrats and Republicans to abolish ice, (including
members of ice) as a mismanaged over bloated arm of government with more responsibility than it can oversee and too little oversight.
Tacitly making ICE the middle man here when law officers should be handling the case directly won't help.