The capability to safely interrupt business process activities is an important requirement for advanced processaware information systems. Indeed, exceptions stemming from the application environment often appear while one or more application-related process activities are running. Safely interrupting an activity consists of preserving its context, i.e., saving the data associated with this activity. This is important since possible solutions for an exceptional situation are often based on the current data context of the interrupted activity. In this paper, a data classification scheme based on data relevance and on data update frequency is proposed and discussed with respect to two different real-world applications. Taking into account this classification, a correctness criterion for interrupting running activities while preserving their context is proposed and analyzed.