How to place dead creatures on the map.

Every time I moved a character away from a creature, and the character was no longer within its attack range, the creature died, but it was still possible to attack it. Why is that?
And also, how can I make it stay on the map forever?
Thank you for your answer, Pobeditel!

Added 2 minutes later
I didn't notice at the beginning of the topic that there were answers to all my questions... :o :o :o