The description of the speak with dead spell says (emphasis mine):
You grant the semblance of life and intelligence to a corpse of your choice within range, allowing it to answer the questions you pose. The corpse must still have a mouth and can’t be undead. […]
Until the spell ends, you can ask the corpse up to five questions. The corpse knows only what it knew in life, including the languages it knew. […] This spell doesn’t return the creature’s soul to its body, only its animating spirit. Thus, the corpse can’t learn new information, doesn’t comprehend anything that has happened since it died, and can’t speculate about future events.
Let’s say my party is tracking someone with knowledge they need, who unbeknownst to them was betrayed by the big bad, killed, and turned into a wight. Obviously, in wight form he can’t be targeted by the spell, because he’s undead.
Once they slay the wight (assuming there’s enough of the corpse left to talk with), is the resulting corpse still undead, and therefore unable to be the target of the speak with dead spell? Or is he just an ordinary corpse at that point, and this a valid target for the spell? Are dead undead still considered undead, or are they just dead?