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Multilayer systems are coupled networks characterized by different contexts (layers) of interaction and have gained much attention recently due to their suitability to describe a broad spectrum of empirical complex systems. They are very fragile to percolation and first-neighbor failure propagation, but little is known about how they respond to non-local disruptions, as it occurs in failures induced by flow redistribution, for example. Acknowledging that many socio-technical and biological systems sustain a flow of some physical quantity, such as energy or information, across the their components, it becomes crucial to understand when the flow redistribution can cause global cascades of failures in order to design robust systems,to increase their resilience or to learn how to efficiently dismantle them. In this paper we study the impact that different multiplex topological features have on the robustness of the system when subjected to non-local cascade propagation. We first numerically demonstrate that this dynamics has a critical value at which a small initial perturbation effectively dismantles the entire network, and that the transition appears abruptly. Then we identify that the excess of flow caused by a failure is, in general, more homogeneously distributed the networks in which the average distance between nodes is small.Using this information we find that aggregated versions of multiplex networks tend to overestimate robustness, even though to make the system more robust can be achieved by increasing the number of layers. Our predictions are confirmed by simulated cascading failures in areal multilayer system.