In go, does a live group with 2 eyes survive being surrounded by the other players stones or are the stones in that live group dead?
If I invade my opponent's surrounded territory with just 1 stone, does my opponent have to play 3 stones to remove me? If I am not removed he is no longer surrounding the territory because my 1 stone means the territory is not surrounded entirely by my opponent's stones.
A group with two true eyes (not "false eyes") is and remains alive even if surrounded by the other player, and cannot be captured by an sequence of moves by the other player. That is what being a "living group" means.
An invading stone that is not able to be included in a living group will be considered dead at the end of the game, and its stone will be treated as having been captured. If black invades a white group and white must answer each move to prevent black from creating a living group, then the net score will be unchanged. If white can safely leave black's plays unanswered without black being able to form a living group, black will lose a point for each such move. But if white is in error and black can make a living group, or cut off a white group and connect to a living group, black will make significant profit.
If the players do not agree on whether a group is alive or not, play is not over; if the disagreement is only discovered while scoring, play is resumed to settle the status of the group(s) in question.