  We study how stability can be maintained even after any set of at most k
players leave their groups, in the context of hedonic games. While stability
properties ensure an outcome to be robust against players' deviations, it has
not been considered how an unexpected change caused by a sudden deletion of
players affects stable outcomes. In this paper, we propose a novel criterion
that reshapes stability form robustness aspect. We observe that some stability
properties can be no longer preserved even when a single agent is removed.
However, we obtain positive results by focusing on symmetric friend-oriented
hedonic games. We prove that we can efficiently decide the existence of robust
outcomes with respect to Nash stability under deletion of any number of players
or contractual individual stability under deletion of a single player. We also
show that symmetric additively separable games always admit an individual
stable outcome that is robust with respect to individual rationality.
