Purifying the World allows an investigator to collect the monster tiles of defeated monsters and then flip the card to perform some action based on the number or toughness of tiles he's collected. Can the investigator collect, or probably more appropriately keep track of, monsters which do not simply go back to the drawing pile, for instance ones that are set aside on the ancient one and used repeatedly in mysteries and encounters? My thinking is that the most sensible thing to do is return them to their source (i.e. the ancient one sheet instead of making them "unavailable") and keep track of them mentally or on paper to count them when flipping the Purifying the World card.
As luck would have it there is an official answer on this from the game designer:
The Purifying the World Unique Asset as well as the Hunting the Thousand Mystery allow investigators to “keep” defeated non-Epic Monsters. Both of these effects will function whether the Combat Encounter was premeditated or an ambush and even if the Monster is to be set aside.
It works like this: A Monster ambushes an investigator. He defeats it and instead of discarding it as normal, he places it on the Mystery or his TASK. While on that card, it is not available to be spawned, but its attributes may be referenced to resolve another ambush in the future.
If another investigator were ambushed by a Monster, and the only available reference for that Monster has been placed on another card, that investigator would not be able to “keep” that Monster on his own Purifying the World; that specific token is already claimed.
Finally, if a Monster that was previously set aside has been placed on a card, it will return to being set aside instead of being discarded when that card is discarded or otherwise removed from play.
Thanks for playing!
~ Nikki Valens
Fantasy Flight Games
Summary: yes you can place such monsters on Purifying the World. Once you eventually turn that card over (or lose it for some reason), those monsters go back to being put aside.
It seems it is an intentional secondary effect of this asset to enable you to remove monsters from the game! (At least until you flip over or lose the card)