When a neural network is partitioned and distributed across physical nodes, failure of physical nodes causes the failure of the neural units that are placed on those nodes, which results in a significant performance drop. Current approaches focus on resiliency of training in distributed neural networks. However, resiliency of inference in distributed neural networks is less explored. We introduce ResiliNet, a scheme for making inference in distributed neural networks resilient to physical node failures. ResiliNet combines two concepts to provide resiliency: skip connection in residual neural networks, and a novel technique called failout, which is introduced in this paper. Failout simulates physical node failure conditions during training using dropout, and is specifically designed to improve the resiliency of distributed neural networks. The results of the experiments and ablation studies using three datasets confirm the ability of ResiliNet to provide inference resiliency for distributed neural networks.