They remain undead but are now free-willed.
In the vampire entry in the monster manual, the section on vampire spawn states:
Vampire spawn become free-willed when their creator dies.
In particular, in Curse of Strahd, the aftermath section also states that (spoilers, emphasis mine):
Upon his death, Strahd's vampire spawn are freed from his control, and each seeks a new destiny. Escher, in particular, leaves the realm, in search of new experiences and a way to become a vampire lord himself.
This further suggests that spawn would remain undead even after their creator's death.