Static Net

Although all the cards in The Brothers' War that create Powerstone tokens create a tapped Powerstone token, entering the battlefield tapped isn't part of the token's definition. Notably, if you create a token that is a copy of a Powerstone token, the token copy won't enter the battlefield tapped.

If Static Net leaves the battlefield before its first ability resolves, the target permanent won't be exiled.

Powerstone tokens are a kind of predefined token. Each one has the artifact subtype "Powerstone" and the ability "{T}: Add {C}. This mana can't be spent to cast a nonartifact spell."

In a multiplayer game, if Static Net's owner leaves the game, the exiled card will return to the battlefield. Because the one-shot effect that returns the card isn't an ability that goes on the stack, it won't cease to exist along with the leaving player's spells and abilities on the stack.