The decision to investigate and take a foreigner into custody depends upon the discretion of the DHS/ICE. Some foreigners may be less of a priority than others for obvious reasons. The priority of the DHS is focus on those who it can reasonably prove are violating their status. Often, those previously deported and who have more serious criminal convictions are higher value targets. If a person is in police custody or imprisoned, then the DHS may more easily discover them and take action.
Those employers who seem to be knowingly hiring large numbers of unlawful foreigners are another priority.
Your target may not be of as much interest to Immigration and Customs Enforcement, but you can contact them by looking up a local number at www.ice.gov.