Good question and nice to see a quality thread. We currently do not know exactly what happens when vampires die. But considering they are products of his creation and he has a thing for "corrupted souls", depending on your point of view on corruption, then it is plausible he does claim their souls to his realm. Pureblooded female vampires are known as "Daughters of Coldharbour.", so from that we know that they are tied to his sphere and his realm.
There are similarities to vampires and Molag Bal as there is to vampires and Hircine. For example, vampirism us a curse/blessing and a disease. Totems of Hircine are artifacts given to werewolves by Hircine to grant them more power, as is the same for Molag Bal and his vampiric artifacts. While Sheogorath can claim the souls of madmen and Malacath is implied to do the same, we can be certain that Molag Bal does work the same for his own creations. Nords go to Sovngarde for being valient and thus Shor is heavily involved with their culture, I suppose Coldharbour is the vampire afterlife.
Now what happens when they are claimed? I do not know. Hircine's werewolves hunt with him at night as mentioned in Infernal City and some see it as a paradise. Though depending on the situation, they can be hunted as well. As for Molag and vampires, it is said that those who venture into his realm are kept in charnel houses and prisons, even though Bal himself may not be so punishing towards vampires if they honored him and served him in their lifetimes.