Castro did exactly that during the Cuban Boat Lift 1980:
http://www.independent.co.uk/news/criminals-in-exodus-from-cuba-us-fears-castro-emptying-his-jails-into-florida-1386288.html
"Officials in Washington say they have learned from sources in Havana that, the releases from Cuban prisons began last weekend. President Bill Clinton is acutely conscious of the effectiveness of the Cuban tactic of sending killers and thieves along with genuine refugees: in 1980 his own political career was almost ended when 18,000 Cuban boat people, mostly former prisoners, rioted at a US military base, Fort Chafee in Arkansas."
Cuba’s solution becomes the U.S.’s problem
Moreover, Castro wanted to create problems for the U.S. while solving problems in Cuba. He had many of the street crime and even murder prisoners in jails as well as some political prisoners and the patients in mental hospitals and asylums transported to Mariel. He forced the Cuban-Americans to take several of his problem cases for each relative he allowed them to take.
As we realized Cubans were being landed up and down the Florida Keys as well as in Miami by the thousands, most were not relatives, and worse many were common criminals or insane, we began to see we were facing an invasion of a type never envisioned in our worst nightmare. Of course none of these Cubans newly arriving in the U.S. had visas; most had no documents, and there was no way to figure out who most really were. Mixed in were the mothers, fathers, aunts, and children of the Cuban exiles, but many of them also had no documents.
