When Purifying the World, can you keep or track monsters you don't usually return to the drawing pile?
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)