Is any reference made anywhere in Tolkien's novels about the number of Balrogs in existence after the demise of the Balrog of Moria? Since Balrogs are described as powerful magical entities that even Gandalf feared, I am assuming that they were created specifically by Morgoth, rather than being a natural species that extend their existence via procreation.
Is there any documentation of a specific number of Balrogs in existence at any one time or any details as to what they specifically are?
Balrog1 are Maiar2 that were "scourges of fire". They were seduced by the evil Vala Melkor (Morgoth)3, who corrupted them to his service in the days of his splendour before the making of Arda.
"Is there any documentation of a specific number of Balrogs in existence at any one time or any details as to what they specifically are?"
The specific number is never mentioned, and it is also not mentioned that the Balrog of Moria is the last. This essay explains how the number of Balrogs has changed since they were first written about by Tolkien. While Christopher Tolkien has written seven as the final number, there are instances in canon where they are described as thousands. Additionally the Quenta Silmarillion describes how
"The Balrogs were destroyed, save some few that fled and hid themselves in caverns inaccessible at the roots of the earth."
Which may indicate that there were more than just the one left in Middle-earth.
The Timeline of Arda4 mentions only the Dagor Dagorath5 (Last Battle) after the events in The Lord of the Rings, and does not make any mention of Balrogs participating in it.
Yes.
The number of Balrogs has changed in Tolkien's mind. In the beginning there were thousands of them, and they were quite weak. For instance, when Fëanor is surrounded by Balrogs, Tolkien thought of them as far weaker and numerous than in later writings, such as The Lord of the Rings.
Morgoth flees from Valinor with the Silmarils, the magic gems of Fëanor, and returns into the Northern World and, rebuilds his fortress of Angband beneath the Black Mountain, Thangorodrim. He devises the Balrogs and the Orcs. The Silmarils are set in Morgoth's iron crown
It is notable that the Balrogs were still at this time, when The Lord of the Rings had been completed, conceived to have existed in very large numbers (Melkor sent forth 'a host of Balrogs');
Those are quotes from The History of Middle-Earth (HoME).
In the end, he decided that there were seven of them.
In the last version, the balrogs are Maiar who were attracted by Morgoth's power and corrupted by him. So they do not reproduce (only Melian among the Maiar did), nor were they created by Morgoth.
Orcs are beasts and Balrogs corrupted Maiar.
Note that we only know the number of Balrogs through Christopher Tolkien, who compiled his father's writing. However it's quite obvious when reading The Silmarillion that they grow stronger. In some earlier versions there are entire armies of Balrogs, which would be ridiculous – were they as powerful as shown in The Lord of the Rings.
All that info comes from HoME, which is not completely canonical, as it's not approved for publication by Tolkien.
Edit1: see Lost Tales, Part II, "The Fall of Gondolin"
Edit2: There is some commentary in the Lost Tales about the number of Balrogs, but nothing about the number seven. If anyone knows where the exact quote is, please edit this answer.
Edit3: I have it!
'a host of Balrogs, the last of his servants that remained' ) 'his Balrogs, the last of his servants that remained faithful to him'. In the margin my father wrote: 'There should not he supposed more than say 3 or at most 7 ever existed.'
From HoME. It's written by Tolkien but never published.
Actually, at least one may have survived, and many games use this hypothesis.
We know that there were 7 of them.
Gothmog was killed by Ecthelion. Another was killed by Glorfindel. And another one, Durin's Bane, was kllled by Gandalf in the Third Age.
Finally, Tolkien writes that most of the Balrogs were killed in the War of Wrath.
So in the War of Wrath there were 5 alive, and most of them, at least 3, were killed.
This means that it is possible that 2 survived, one being Durin's Bane.
So there is the possibility of one unnamed Balrog alive in the Fourth Age.
