Resilience assessment is a widely-used tool to evaluate the ability of an object (e.g., an individual structure, or a system consisting of multiple interacting structures) to withstand, recover from, and adapt to disruptive events. This paper proposes a novel concept of “nonresilience curve”, which measures the nonresilience (complement of resilience) of an object of interest conditional on a specific hazard intensity. It is by nature an extension of the well-established fragility curves, integrating the multiple damage states of a post-hazard object. The applicability of the proposed nonresilience curve to individual structures and systems (including series systems, parallel systems, and more general & complicated systems) has been demonstrated in this paper. It is also preliminarily shown that the shape of the cumulative distribution function of a lognormal distribution is suitable to approximate the nonresilience curve, if only limited data points associated with the target nonresilience curve are available. Since the nonresilience curve is a function of the hazard intensity measure, one can estimate the nonresilience of an object in a fully probabilistic manner by additionally taking into account the uncertainty associated with the intensity measure. The proposed nonresilience curve can be further extended to formulate nonresilience surface, which is a joint function of both the intensity measure and the available resource that supports the post-hazard recovery process. The nonresilience curve is promising to be adopted in engineering practice for resilience assessment and resilience-based design of civil structures and infrastructures.