What the hell does immigration status have to do with an insurance claim? Wut? Lol

The cops aren't going to ask for a valid visa for any type of accident. You don't have to have a valid visa to get a drivers license even for a car in NYC.

But the cops aren't even going to come for a bike accident unless someone is very hurt or there's more than $500 worth of damage. They wont even come for a car accident with minor damage. The only time your immigration status may matter is if you are charged with a crime after an crash which happens very rarely. Is it possible there has been a case where an undocumented delivery guy was working shit faced drunk and ran over another delivery guy and killed them? I guess it's possible but it's never happened. At least not to my knowledge.