Social disruptions caused by the COVID-19 pandemic challenged existing institutional arrangements that govern the society. During that time, nation-states had to prevent the collapse of society and rapidly establish new institutions and adapt existing ones to address public health, job security, and freedom-of-movement concerns. At the same time, institutional developments are explicitly or implicitly related to the cultural and moral values relevant to societal well-being. Values hold a significant role in governing society during crises, guiding states' institutional response to unforeseen challenges. However, values themselves are not static: research has shown that values may change rapidly during crises. This paper studies the relationship between value change and institutional change in times of crisis using agent-based modelling and machine learning techniques. In our model, we represent countries as agents who define institutional strategies to control disease spread and subsequently protect the well-being of their citizens. Institutional change and value change are modelled as two independent processes. Yet, the model confirms the seemingly trivial inverse correlation between them: when the value of openness-to-change increases in a society, the institutional strategies also become less strict. Conversely, when conservatism increases, the strategies become stricter on average. However, there is no direct causal relationship between the two changes: being open to change does not necessarily make a government select more relaxed rules, but this correlation is rather an emergent consequence of being more flexible in changing rules, whether the new ones are stricter or more relaxed.