Expands mandatory immigration detention to include noncitizens who are inadmissible under specified INA provisions and who are charged with, arrested for, convicted of, or admit to acts that constitute burglary, theft, larceny, or shoplifting; it also requires Department of Homeland Security (DHS) to issue a detainer and take custody of those individuals. Separately, it gives State attorneys general (or other authorized State officers) a private right to sue federal officials in U.S. district court when certain immigration detention, removal, parole, or visa decisions injure the State or its residents, requires courts to expedite those cases, and creates a limited exception to a general injunction limitation rule.