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I tried it as you described here, but it still doesn't work because the monster remains highlighted, and the arrow still points to it. Basically, it's still a monster, you just can't fight it.
I did it this way: I took a developer object – a picture. I left it on the map, went into the shared section, copied the current object that belonged to that picture, and then specified the Model and AnimSet parameters of the monster I wanted for it.
And after that, I added the death script described above. As a result, the corpse just lies there, and you can't interact with it in any way; it's just like a background element.