If a monster's entry doesn't state what happens to a drained victim, it becomes a wight. See the energy drain description in the DMG.
Here's a related question. The vampire and vampire spawn entries talk about the monsters' coffins, and how they try to get back to their coffins after being "killed". Suppose we have a bunch of hapless adventurers who fight a vampire, and they all get drained to death. No-one is around to bury them. Do they have coffins? What happens if they get reduced to zero hit points?