As deep neural networks continue to expand and become more complex, most edge devices are unable to handle their extensive processing requirements. Therefore, the concept of distributed inference is essential to distribute the neural network among a cluster of nodes. However, distribution may lead to additional energy consumption and dependency among devices that suffer from unstable transmission rates. Unstable transmission rates harm real-time performance of IoT devices causing low latency, high energy usage, and potential failures. Hence, for dynamic systems, it is necessary to have a resilient DNN with an adaptive architecture that can downsize as per the available resources. This paper presents an empirical study that identifies the connections in ResNet that can be dropped without significantly impacting the model's performance to enable distribution in case of resource shortage. Based on the results, a multi-objective optimization problem is formulated to minimize latency and maximize accuracy as per available resources. Our experiments demonstrate that an adaptive ResNet architecture can reduce shared data, energy consumption, and latency throughout the distribution while maintaining high accuracy.