* The Killing Curse is a soul-destroying spell. It doesn't just end life, it obliterates the soul, leaving behind an empty shell. This means there's nothing left for the Imperius Curse to control.
* The Imperius Curse requires a living target. The curse works by forcing someone's will into submission. A dead person doesn't have a will to be controlled.
* The Imperius Curse is about mind control, not resurrection. Even if it could work on a dead person, it wouldn't bring them back to life. It would only manipulate their lifeless body.
In short, attempting to use the Imperius Curse on someone who has been killed by the Killing Curse would be pointless. There is no magical or logical way for the curse to work on a deceased target.
It's important to remember that these are the rules of the fictional world established by J.K. Rowling. In real life, there are no such spells or curses, and death is a permanent end to life.