Unlike traditional methods that assume removals are independent of the failure process, this paper presents a novel approach for classical and Bayesian inference under progressive Type-II censoring with informative random removals. Under a Weibull-Poisson lifetime model, two removal distributions—the truncated Poisson and truncated discrete Weibull—are introduced. Due to their structural dependence on the model parameters, these distributions enhance estimation accuracy under heavy censoring. Finally, the superiority of the proposed methods is evaluated through Monte Carlo simulations and the analysis of real data on remission times of bladder cancer patients.