In this paper, we develop a conditional copula model to analyze the distribution of a claim that generates different types of costs and/or simultaneously impacts several guarantees. Our methodology is adapted to taking into account the particular structure of our data, since observations are subject to right-censoring. Right-censoring occurs since payment of a claim is not made instantaneously, and therefore unsettled claims only provide a partial information on the phenomenon that one wishes to model. The new methodology that we develop is supported by theoretical results that show the asymptotic normality of our estimators. A simulation study and a real data analysis illustrate the method.