Distributed graph processing systems largely rely on proactive techniques for failure recovery. Unfortunately, these approaches (such as checkpointing) entail a significant overhead. In this paper, we argue that distributed graph processing systems should instead use a reactive approach to failure recovery. The reactive approach trades off completeness of the result (generating a slightly inaccurate result) while reducing the overhead during failure-free execution to zero. We build a system called Zorro that imbues this reactive approach, and integrate Zorro into two graph processing systems - PowerGraph and LFGraph. When a failure occurs, Zorro opportunistically exploits vertex replication inherent in today's graph processing systems to quickly rebuild the state of failed servers. Experiments using real-world graphs demonstrate that Zorro is able to recover over 99% of the graph state when 6-12% of the servers fail, and between 87- 95% when half the cluster fails. Furthermore, using various graph processing algorithms, Zorro incurs little to no accuracy loss in all experimental failure scenarios, and achieves a worst-case accuracy of 97%.