Privacy-preserving inference in edge computing paradigms encourages the users of machine-learning services to locally run a model on their private input and only share the models outputs for a target task with the server. We study how a vicious server can reconstruct the input data by observing only the models outputs while keeping the target accuracy very close to that of a honest server by jointly training a target model (to run at users' side) and an attack model for data reconstruction (to secretly use at servers' side). We present a new measure to assess the inference-time reconstruction risk. Evaluations on six benchmark datasets show the model's input can be approximately reconstructed from the outputs of a single inference. We propose a primary defense mechanism to distinguish vicious versus honest classifiers at inference time. By studying such a risk associated with emerging ML services our work has implications for enhancing privacy in edge computing. We discuss open challenges and directions for future studies and release our code as a benchmark for the community at https://github.com/mmalekzadeh/vicious-classifiers .