We all still die.
Everyone dies, including warrior cats. Some cats get looked over when they die. For others, their pain and suffering will forever echo across the ages.
Cat's can't die twice.
That's where the Hunter's screwed up. Just from the amount of protest is evidence enough to show that this is ridiculous.
Instead, cat's are born again.
If cats are reborn, and if the Hunters had followed a path of logic that made sense, we would be seeing some familiar faces later in the series.
Spottedleaf, Tigerstar, and Hawkfrost. Walking among us again.