The Feign Death spell (PHB, p. 240) says:
For the spell’s duration, or until you use an action to touch the target and dismiss the spell, the target appears dead to all outward inspection and to spells used to determine the target’s status.
The Animate Dead spell, on the other hand, says:
This spell creates an undead servant. Choose a pile of bones or a corpse of a Medium or Small humanoid within range. Your spell imbues the target with a foul mimicry of life, raising it as an undead creature. The target becomes a skeleton if you chose bones or a zombie if you chose a corpse (the DM has the creature's game statistics).
Feign Death has this strange clause that all spells used to detect the target status register it as being dead. Animate Dead takes a corpse of a dead creature and create a zombie out of it.
On one hand, a Feigned creature isn't a corpse, so it isn't a valid target for Animate Dead. On the other hand, if Animate Dead fails, then the creature isn't a corpse, but that would violate the clause from Feign Death that says the target appears dead to spells used to determine the target status and now my head is hurting and I don't understand anything anymore.
What happens if you cast Animate Dead on a creature currently under effect of Feign Death to determine if it is dead?
Would you end up with some weird living zombie that is undead but not really?