It seems there's been a rumor going around since early last year concerning the perhaps-too-popular kiddie-world Webkinz. The story goes that some sort of malware can 'kill your Webkinz' inside the game. The accounts vary, but many seem to come back to an evil version of one of the in-game NPCs coming after your huggable critters with a weapon. While the image of a chainsaw-wielding duck is evocative, Snopes sets things to right: it's completely untrue.
The site categorizes these rumors as expressions of anxiety over treasured friends/objects; much like a young person would fear a bully ripping the head of their stuffed animal off in real life, so they fear the virtual equivalent. And no, they note, neither Club Penguin nor NeoPets have anything to do with these rumors.