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Many Cyber-Physical Systems (CPS) have timing constraints that must be met by the cyber components (software and the network) to ensure safety. It is a tedious job to check if a CPS meets its timing requirement especially when they are distributed and the software and/or the underlying computing platforms are complex. Furthermore, the system design is brittle since a timing failure can still happen e.g., network failure, soft error bit flip, etc. In this paper, we propose a new design methodology called Plan B where timing constraints of the CPS are monitored at the runtime, and a proper backup routine is executed when a timing failure happens to ensure safety. We provide a model on how to express the desired timing behavior using a set of timing constructs in a C/C++ code and how to efficiently monitor them at the runtime. We showcase the effectiveness of our approach by conducting experiments on three case studies: 1) the full software stack for autonomous driving (Apollo), 2) a multi-agent system with 1/10th scale model robots, and 3) a quadrotor for search and rescue application. We show that the system remains safe and stable even when intentional faults are injected to cause a timing failure. We also demonstrate that the system can achieve graceful degradation when a less extreme timing failure happens.