The concept of the achievable quality of control for a given process has been defined as dynamic resiliency and also often referred to as process controllability. It has been shown in the past that limitations on the dynamic resiliency are imposed by inherent process characteristics. For multi-input multi-output (MIMO) processes, such limitations are imposed by "unstable" zeros of the process transfer matrix, with zeros of individual elements or of submatrices playing no role. In this paper we show that when the satisfaction of dynamic hard output constraints is included in the definition of control quality, zeros of process subsystems affect dynamic resiliency, in the sense that they can cause instabilities in some cases, if the attempt is made to satisfy such constraints. The interplay of input and output constraints is discussed. A quadratic form of Model Predictive Control (MPC) is used for on-line control, but it is shown that the results are independent of the tuning parameters. Several theorems are given to establish these results and they are illustrated on examples based on the heavy oil fractionator of the Shell Standard Control Problem.