Final answer:
The facility operated by ICE for initial processing of undocumented migrants is called a processing center, and it is used for intake and classification.
Step-by-step explanation:
The type of immigration detention facility operated by ICE, used to conduct intake, classification, and initial processing of undocumented migrants, is a processing center. This reflects the function of such centers in managing the flow of people entering the country, similar to historical examples like Angel Island in San Francisco Bay, which served to control the flow of Chinese immigrants into the United States.
Modern-day immigration issues have led to both temporary holding facilities and detention centers where undocumented migrants might be held. The intake process at these facilities includes steps intended to manage the identification and necessary legal processing of individuals who have crossed the border.