They don’t have jurisdiction and the State can’t suddenly grant it.

Section 439 of the Antiterrorism and Effective Death Penalty Act of 1996 added a new 8 U.S.C. § 1252c which provides that notwithstanding any other provision of law, to the extent permitted by relevant State and local law, State and local law enforcement officials are authorized to arrest and detain an individual who (1) is an alien illegally present in the United States; and (2) has previously been convicted of a felony in the United States and deported and left the United States after such conviction, but only after the State or local law enforcement officials obtain appropriate confirmation from the Immigration and Naturalization Service of the status of such individual and only for such period of time as may be required for the Service to take the individual into federal custody for purposes of deporting or removing the alien from the United States.

This violates federal law because they are arresting at will.