An intertwined supply network (ISN) is an entirety of interconnected supply chains (SC) which, in their integrity secure the provision of society and markets with goods and services. The ISNs are open systems with structural dynamics since the firms may exhibit multiple behaviors by changing the buyer-supplier roles in interconnected or even competing SCs. From the positions of resilience, the ISNs as a whole provide services to society (e.g., food service, mobility service or communication service) which are required to ensure a long-term survival. The analysis of survivability at the level of ISN requires a consideration at a large scale as resilience of individual SCs. The recent example of coronavirus COVID-19 outbreak clearly shows the necessity of this new perspective. Our study introduces a new angle in SC resilience research when a resistance to extraordinary disruptions needs to be considered at the scale of viability. We elaborate on the integrity of the ISN and viability. The contribution of our position study lies in a conceptualization of a novel decision-making environment of ISN viability. We illustrate the viability formation through a dynamic game-theoretic modelling of a biological system that resembles the ISN. We discuss some future research areas.