Using access to a unique bank loss database, we find positive dependencies of default resolution times (DRTs) of defaulted bank loan contracts and final loan loss rates (losses given default, LGDs). Due to this interconnection, LGD predictions made at the time of default and during resolution are subject to censoring. Pure (standard) LGD models are not able to capture effects of censoring. Accordingly, their LGD predictions may be biased and underestimate loss rates of defaulted loans. In this paper, we develop a Bayesian hierarchical modelling framework for DRTs and LGDs. In comparison to previous approaches, we derive final DRT estimates for loans in default which enables consistent LGD predictions conditional on the time in default. Furthermore, adequate unconditional LGD predictions can be derived. The proposed method is applicable to duration processes in general where the final outcomes depend on the duration of the process and are affected by censoring. By this means, we avoid bias of parameter estimates to ensure adequate predictions.