Yeah, I looked into it, and ICE actually has two distinct components: Homeland Security Investigations (HSI) and Enforcement and Removal Operations (ERO). Pretty much everyone things ICE == ERO, so you've got stuff like Canadians agitating to close the HSI collaboration offices in Canada.
Well and unfortunately until recent times ERO was mostly dedicated to criminals first and other folks second but my understand was there was a backlog of criminals to find, capture and remove that person he other parts were less of a concern.