An important feature of a digital organization is its ability to change rapidly. For an organization to remain capable of rapid change, it must be on the brink of resilience, since a resilient organization always resists change. The article examines the borderline state of the organization, which is on the verge of its stability and instability. In this state, the organization begins to lose predictability in the details of behavior, but still retains predictability in general. The authors called this borderline state the statistical sustainability of the organization. The phenomenon of statistical sustainability of an organization is very similar to the property of stability of the frequency of mass events and average values ​​described in mathematical statistics by a similar term. To analyze the nature of the statistical sustainability of the organization, the authors used the ideas of strange attractors and modes with sharpening from the theory of complex systems. A strange attractor is an area of ​​the organization’s behavior that, outside this area, is an area of ​​stability for the organization, and inside it is an area of ​​complete unpredictability. The theory of complex systems has shown that it is in the regions of strange attractors that the conditions for the variability of systems are created, and the theory of modes with aggravation shows the conditions under which this variability can lead to self-organization, that is, the spontaneous emergence of new structures. This article shows that systematic digitalization objectively leads to the formation of the statistical sustainability of the organization and creates the preconditions for maintaining the organization’s ability to make rapid changes. In traditional management, the statistical sustainability of an organization is viewed as a threat and a source of risk. Therefore, in the context of systematic digitalization, traditional approaches to management should be significantly refined.