The rapid development of artificial intelligence (AI) has changed social institutions, introducing new opportunities, as well as new threats, to the field of criminal responsibility that have never been previously witnessed. The more AI systems work beyond national borders, be it in financial, healthcare, educational, or governmental fields, the more they allow offences that are difficult to conceptualize in terms of liability, jurisdiction, and accountability. In this paper, the dynamics of cross-border criminal responsibility during the era of AI are viewed through the lens of how the law and the institutions of society have to evolve to accommodate AI-assisted crimes. The study employs a theoretical, normative, and interdisciplinary methodology, combining jurisprudence with social science perspectives to analyze institutional trust, human behavior, and global governance. The analysis begins by placing AI in transnational contexts where crimes like online fraud, deepfaking, and algorithmic bias are not limited by national borders and destroy the integrity of institutions. Legal principles cannot be used to reflect the socio-political aspects of such offences, and therefore, social science perspectives should be integrated. Social institutions such as courts, regulatory authorities, education systems and community organizations are places of vulnerability and sources of resilience. Their role needs interdisciplinary studies that involve combining jurisprudence with knowledge about human behaviors, institutional trust, and global governance. Three dimensions are examined, namely, the attribution of criminal responsibility in cases where AI systems behave autonomously or in a manner that cannot be predicted by their designers; second, conflicts of jurisdiction and enforcing cross-border, diffuse, and decentralized offences; and third, the part played by social institutions in setting ethical standards, building accountability, and enforcing justice. Finally, the paper proceeds to advance the position that AI needs to engage in transnational collaboration, interdisciplinary dialogue, and rights-oriented approaches. Societies can only address the disruptive potential of AI by introducing justice and accountability into social institutions and protecting cross-border resilience and trust.