2018-10-05 : If the permanent’s controller doesn’t search their library, they don’t shuffle their library.

2018-10-05 : If the target permanent is a legal target but isn’t destroyed, most likely because it has indestructible, its controller may search their library.

2018-10-05 : If the target permanent is an illegal target by the time Assassin’s Trophy tries to resolve, the spell doesn’t resolve. No player searches their library.