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?