An important characteristic of distributed object management systems is that due to network or machine failure, the environment may become partitioned into subenvironments that cannot communicate with each other. In some application scenarios, it is important that the subenvironments remain operable even in this case. In particular, queries should be processed in an appropriate way. To this end, the final and all intermediate results of a query in a distributed object management system must be regarded as potentially vague. We propose a hybrid representation for vague sets and vague multisets designed for this application context. The representation consists of an enumerating part, which contains the elements we could access during query processing, and a descriptive part, which describes the relevant elements we could not access. We introduce propagation rules which can be used to minimize the vagueness of a query result represented in this hybrid way. The main advantage of our approach is that the descriptive part of the representation can be used to improve the enumerating part during query processing.