Never said suddenly. Eventually.

Also I think a more apt comparison would be if the ISS would leave the solar system if the earth stopped. Since the sun is 333,000 times more massive than the earth and the moon is only 1/80 the mass of the earth. Not sure if the moon would escape the solar system but it would definitely be yeeted a ways out of Earth’s orbit. Since the earth disappearing basically forces an orbital slingshot maneuver. The ISS would probably escape the solar system if it didn’t encounter the Gas Giants.