Dwindling and mixing with lesser men does not mean one is no longer a Dúnadan. Take for example King Eldacar who was the 21st King of Gondor. His mother was a Northwoman. If one were to look at dwindling of the the peers of the Black Númenóreans in Gondor and in Arnor I'd say they dwindled because they did not have a lot of children, had children late in life, or none at all, and because their homeland was destroyed. The dwindling of the Númenóreans
was not a normal tendency, shared by the peoples who proper home was
Middle-earth, but do to the loss of their ancient land far in the
West, nearest of all mortal lands to the Undying Realm. [Númenórean
Death from war and disease would also contribute to their dwindling as a people. Most, if not all of the Dúnedain at the end of the 3rd Age were mixed to some degree, including Aragorn. Perhaps with Sauron whispering in their ear the Black Númenórean who had been under his sway from the beginning somehow avoided this.
Generally the Black Númenórean would be those who were part of the King's Men faction in Númenor. They "sailed far away to the south; and the lordships that they made have left many rumours in the legends of Men." [Akallabeth] They abandoned speaking Eldarin tongues and spoke Adunaic [Appendix F: Of Men].
During the Kin-strife in Gondor those who escaped were also what you call Black Númenórean. These rebel kings
never ceased to make war on Gondor since the death of Kastamir,
attacking its ships and raiding its coast at every opportunity. They
had however become much mixed in blood through admission of the Men of
Harad, and only their chieftans, descendants of Kastamir, were of
Numenorean race. [Heirs of Elendil]
In 1448 they took Umbar for themselves and almost 400 years later in 1810 Telumehtar destroyed the last descendants of Castamir. Interestingly some of Castamir's kin mixed with non-Dúnedain women after fighting their cousins in the royal house for mixing with non-Dúnedain.
There was also a royal wedding between a Black Númenórean and the 12th King of Gondor. This is also slightly significant, if you did not know better, because the Kings of the Dúnedain only married other Dúnedain up until Valacar who married a Northwoman named Vidumavi.
it was a thing unheard of before that the heir to the crown , or any
son of the King, should wed one of lesser and alien race. [Gondor and
the Heirs of Anárion]
Valacar was the 20th King of Gondor and was the first to take a wife not of Dúnedain descent and hence the onset of the Kin-strife. Beruthial, who was a "Black Númenórean" was accepted because she was also of Dúnedain descent.
Beruthial married Tarannon and she was his "nefarious, solitary, and loveless wife" [Unfinished Tales; The Istari; Note 7]. She was eventually put out to sea with her cats and her name erased from the Book of the Kings.
The Mouth of Sauron himself may simply have been another of these renegade Gondorian Dúnedain,
But it is said that he was a renegade, son of a house of wise and
noble men in Gondor, who becoming enamoured of evil knowledge entered
the service of the Dark Tower, and because of his cunning [and the
fertile cruelty of his mind] [and servility] he grew ever higher in
the Lord's favour [The War of the Ring: The Black Gates Open].
There are thus the King's Men who took up in the South and East, Castamir's kin who fled the Kin-strife to Umbar, other nobility taking up with Sauron like his Mouth, and also members of the royal house heading South to join the rebels to escape the watchful and threatening eye of their kin who held the throne.
the descendants of the kings had become few. Their numbers had been
greatly diminished in the Kin-strife; whereas since that time the
kings had become jealous and watchful of those near akin. Often those
on whom suspicion fell had fled to Umbar and there joined the rebels; [Gondor and the Heirs of Anárion]
More likely than not the Black Númenóreans were also mixed to some degree, but those who had avoided what some of Castamir's kin did in "married the women of Harad and had in three generations lost most of their Númenórean blood" [The Heirs of Elendil] were the genuine Black Númenórean. I do not think I've come across someone in the tales with the appellation Númenórean or Dúnedain who was not actually one of the Men of the West. For example, Éowyn's grandmother Morwen was a Dúnadan woman, but Éowyn and her brother are not Dúnedain themselves. They are quite too mixed for that although she resembled her grandmother, and all of Morwen's descendants were taller than the other Rohirrim.
Númenórean (Quenya) and Dúnedain (Sindarin) mean they same thing, people/men of the west. Númenor means Westland or Westernesse. So a Númenórean is a Dúnedain, as mentioned in Akallabeth, "that people that in the Grey-elven speech are called the Dúnedain: the Númenórean, Kings among Men." These two terms are interchangeable. They mean the same thing in different languages, Númenórean = Dúnedain = Men of the West.