They had a few colonies in Middle-earth, particularly Umbar. They may not have existed after TA 1050, though, after their defeat by Ciryaher. It's possible any survivors joined with the followers of Castamir after the Kin Strife and became the Corsairs of Umbar.
At least a few of the Black Númenóreans made it well into the Third Age or beyond. The Mouth of Sauron ("no Ringwraith but a living man") is said to have been "a renegade, who came of the the race of those that are named the Black Númenóreans; for they established their dwellings in Middle-earth during the years of Sauron's domination, and they worshipped him, being enamoured of evil knowledge. And he entered the service of the Dark Tower when it first rose again, and because of his cunning he grew ever higher in the Lord's favour; and he learned great sorcery, and knew much of the mind of Sauron; and he was more cruel than any orc." Quotes from The Lord of the Rings: The Return of the King, Chapter 10 "The Black Gate Opens".