A person from South Dakota, presuming they are here legally in the first place, is "known" to the government, with few exceptions. He or she may have a criminal record if they are a criminal. They will probably have a school record, a work record, etc. etc. etc. They won't be a complete unknown. If they commit a crime in Florida, the police will access those records which will be probative.
I think the notion we should have completely open borders is absurd.