In the context of reliability assessment, estimating a failure probability associated to a rare event is a common task. To do so, various techniques have been proposed to overcome traditional crude Monte Carlo which becomes intractable in such a context. Among others, Subset Simulation is a widely used technique which relies on "splitting" the rare event probability into a sequence (i.e., a product) of less rare conditional probabilities associated to nested failure events, easier to estimate. However, this technique relies on simulating samples conditionally to the failure event by means of Monte Carlo Markov chain algorithms. These algorithms enable, at convergence, to simulate according to the target density. However, in practice, it often produces non-independent and identically distributed (i.i.d.) samples due to the correlation between Markov chains. In the present work, we propose another way to sample conditionally to the nested failure events in order to get i.i.d. samples which can be required (e.g., to perform dedicated sensitivity analysis). The proposed algorithm relies on a nonparametric fit of the conditional joint distribution using a combined kernel density estimation for marginals fitting and the Empirical Bernstein Copula (EBC). Thus, this new method presents some similarities with "Nonparametric Adaptive Importance Sampling" but addresses the problem of copula fitting by means of EBC. The proposed algorithm is tested on three toy-cases and its performances are compared with those obtained from Subset Sampling.