It is preferred that feature selectors be \textit{stable} for better interpretabity and robust prediction. Ensembling is known to be effective for improving the stability of feature selectors. Since ensembling is time-consuming, it is desirable to reduce the computational cost to estimate the stability of the ensemble feature selectors. % for the data we use. We propose a simulator of a feature selector, and apply it to a fast estimation of the stability of ensemble feature selectors. To the best of our knowledge, this is the first study that estimates the stability of ensemble feature selectors and reduces the computation time theoretically and empirically.