We introduce a novel method for estimating and conducting inference about extreme quantile treatment effects (QTEs) in the presence of endogeneity. Our approach is applicable to a broad range of empirical research designs, including instrumental variables design and regression discontinuity design, among others. By leveraging regular variation and subsampling, the method ensures robust performance even in extreme tails, where data may be sparse or entirely absent. Simulation studies confirm the theoretical robustness of our approach. Applying our method to assess the impact of job training provided by the Job Training Partnership Act (JTPA), we find significantly negative QTEs for the lowest quantiles (i.e., the most disadvantaged individuals), contrasting with previous literature that emphasizes positive QTEs for intermediate quantiles.