Did Voldemort ever find out how Regulus Black died?

Question

As far as I can tell, there seems to be no mention of the how or why of Regulus Black's disappearance by Voldemort or any of the Death Eaters. It should have raised some eyebrows when one of his most devoted young followers just straight up disappeared, with no one, not even his family, knowing what happened to him. I know that Voldemort didn't really care about any of his followers, but I feel like at least one of the Death Eaters would have noticed if the next day Regulus didn't show up for their daily world domination meeting. I could see scrum master Lucius Malfoy saying:

Regulus, how are things going with—Wait, where's Regulus?

If I remember correctly (and according to this answer), after Harry, Ron, and Hermione broke into Gringotts and took Hufflepuff's Cup, Voldemort visited the cave to see if the locket was still there. I think that despite losing his diary Horcrux before regaining his physical body, Voldemort opted not to check in on his other Horcruxes when actually returned to his body due to his arrogance. Under this assumption, the visit after the Gringotts break-in was the first time that Voldemort had visited the cave since he tested its defenses with Kreacher, so naturally he would have assumed that Harry and squad had nabbed it at some point. This means that he likely never found out about Regulus's betrayal through the note Regulus left in the fake locket.

That having been said, did Voldemort ever find out how Regulus Black died? If not, how did he think Regulus died?

Answer 1

Very unlikely

Regulus included a note in the fake locket that Harry and Dumbledore recovered from Voldemort's cave.

"To the Dark Lord,

I know I will be dead long before you read this but I want you to know that it was I who discovered your secret. I have stolen the real horcrux and intend to destroy it as soon as I can. I face death in the hope that when you meet your match you will be mortal once more."

R.A.B

—Harry Potter and the Half-Blood Prince

If Voldemort had found the fake locket before Harry and Dumbledore, he almost certainly would have removed it. Even had he not, it would have been very much out of character for him to leave evidence of his failure (i.e. the note).

And of course, if Voldemort had known how Regulus died, he certainly would have found the fake locket.

What is more, Regulus died in 1979. If Voldemort had learned about Regulus's death before he disappeared (1981), he would have recovered the locket from Grimmauld Place.

There is only really one assumption Voldemort could have made about Regulus's mysterious disappearance: he fled, like Karkaroff. Voldemort would certainly have spent a while trying to track him down, but his parents were dead by this point, and his only living relative was in the Order.

Karkaroff survived an entire year, so Voldemort might not have found it incredible that Regulus could have evaded him for two years.

Answer 2

No - the Dark Lord felt sure no one knew about the Horcrux cave.

The Dark Lord couldn’t have known how Regulus died, because when Harry sees into his mind, he considered the idea that anyone would know about the cave or be able to get past its protection ridiculous - if he’d known how Regulus died then he’d know someone did once before.

“And how could the boy, or anybody else, know about the cave or penetrate its protection? The idea of the locket being stolen was absurd …”
_{^{- Harry Potter and the Deathly Hallows, Chapter 27 (The Final Hiding Place)}}

Also, if he’d known that Regulus had gotten in, then he’d likely at least remember it at this point, when he’s trying to figure out how safe his remaining Horcruxes are. The only possibility that the Dark Lord considers for someone knowing about the lake is that Dumbledore might know.

“The lake, surely impossible … though was there a slight possibility that Dumbledore might have known some of his past misdeeds, through the orphanage.”
_{^{- Harry Potter and the Deathly Hallows, Chapter 27 (The Final Hiding Place)}}

Therefore, the Dark Lord couldn’t have known about how Regulus died - we see directly into his thoughts and it’s clear he thinks that the locket is safe, except possibly from Dumbledore and Harry. If he’d known how Regulus died, he couldn’t be so assured of its safety, since Regulus stole it.