Data loss is often random and unavoidable in realistic networks due to transmission failure or node faults. When it comes to Boolean control networks (BCNs), the model actually becomes a delayed system with unbounded time delays. It is difficult to find a suitable way to model it and transform it into a familiar form, so there have been no available results so far. In this article, the stabilization of BCNs is studied with Bernoulli-distributed missing data. First, an augmented probabilistic BCN (PBCN) is constructed to estimate the appearance of data loss items in the model form. Based on this model, some necessary and sufficient conditions are proposed based on the construction of reachable matrices and one-step state transition probability matrices. Moreover, algorithms are proposed to complete the state feedback stabilizability analysis. In addition, a constructive method is developed to design all feasible state feedback controllers. Finally, illustrative examples are given to show the effectiveness of the proposed results.