Q. How do you kill a zombie?
A. You can't, it's already dead.

Zombies are not running. They have terminated, but they have a living parent who either hasn't waited for them, or hasn't told the kernel that it doesn't want to do that.

Zombies are created because child processes run asynchronously from their parents, and often terminate long before the parent has had a chance to call wait/waitpid on them. The kernel has to keep some minimal information about such child processes in the table so that the parent can have a chance to collect its status, but releases the memory & other resources they might be holding