Wild baby bunnies have a habit of fainting when they get stressed.
When they faint, their muscles all go lax and their head flops around on their neck like it's trying to fall off.
For all appearances, it looks like it's dead...
If this happens, explain to wife that the bunny just couldn't make it and has gone to bunny heaven. Then take the bunny outside to "bury" it. Just put it under a bush in the shade and it will come to and run off. That way you don't have to buy a cage, food, accessories and clean bunny pellets for the next while until it escapes, or gets eaten by the dog.
You'll have the option of telling the wife, "You shouldn't have squeezed it so hard!" or "What'd you do? Break it's neck?" This will keep said adventures from happening again...
The voice of experience...