A Goblin statue is found in Bandos' throne room during and after The Chosen Commander quest. During the quest, the player must climb on some of these statues. After the quest, some of these statues:
Can be fought. At first, it appears to be just a statue. However, if the player attempts to climb on the statue, it will come to life and attack the player. It is the weakest of the four statues that can be found in the room.
Are used in the agility course in the throne room. These cannot come to life and be fought.
Are always just statues (the ones near the portal exit to the room).
Multiple goblin statues can appear at the same spot, if a player takes too long to kill the first and another statue spawns. However, the second statue does not come to life until it is climbed on.
If several players attempt to climb on the same goblin statue at the same time, a separate instance of the statue comes to life and attacks each player. (For example, if three players attempt to climb on the same goblin statue at once, three goblin statues come to life.)
It is possible to be "stuck" underneath one. To do this, you need to log out on top of a respawn point. Once you log back in, you will be stuck under the statue, and unable to move. It is unknown if this was intentional or not.