Adds a new mandatory detention category for certain noncitizens who are inadmissible under specified grounds and who are charged with or admit to burglary, theft, larceny, or shoplifting, and requires the Department of Homeland Security to issue detainers and take custody if they are not already detained. Grants State attorneys general (and other authorized State officers) a new private right to sue federal immigration officials in U.S. district court when specified immigration actions harm the State or its residents, sets a low financial-harm threshold (>$100), and requires courts to expedite those cases.