Shadow Invaders are mobs that will fall from the sky at, what seems to be, random intervals. Typically one invader will spawn per player in the area however it is possible to find one roaming the world that wasn't killed on spawn. These are harder monsters and typically larger monsters than ones you will find roaming the world as well as having a larger swing radius.
Shadow Invaders will always drop loot, sometimes being Tentacles needed to randomize the 3rd & 4th stat on an item. These monsters will agro in the same manner as other monsters, so be aware that while being AFK in your Cornerstone, an invader can still agro you and kill you if he can get close enough.
He can drop rare objects, including, very rarely, pearls of wisdom.