Social groups often exhibit a high degree of dynamism. Some groups thrive, while many others die over time. Modeling destructive dynamics and understanding whether/why/when a person will depart from a group can be important in a number of social domains. In this paper, we take the World of Warcraft game as an exemplar platform for studying destructive group dynamics. We build models to predict if and when an individual is going to quit his/her guild, and whether this quitting event will inflict substantial damage on the guild. Our predictors start from in-game census data and extract features from multiple perspectives such as individual-level, guild-level, game activity, and social interaction features. Our study shows that destructive group dynamics can often be predicted with modest to high accuracy, and feature diversity is critical to prediction performance.