For sustainability, research in operations and supply chain management historically emphasized the development of environmental rather than social capabilities. However, factory disasters in Bangladesh, an emerging market and the second largest clothing exporter in the world, revealed enormous challenges in the implementation of social sustainability in complex global supply chains. Against the backdrop of a building collapse in Bangladesh's clothing industry, this research uses multiple case studies from two time periods to explore the skills, practices, relationships and processes – collectively termed “social management capabilities” (SMCs) – that help buyers and suppliers respond to stakeholder pressures; address regulatory gaps; and improve social performance. The study not only captures the perspectives of both multinational buyers and their emerging market suppliers, but also provides supplementary evidence from other key stakeholders, such as NGOs and unions. Our findings show that, in the absence of intense stakeholder pressure, buyers can lay the foundation for improved social performance by using their own auditors and collaborating with suppliers rather than using third‐party auditors. However, in the face of acute attention from customers, NGOs and media, we observed that consultative buyer‐consortium audits emerged, and shared third‐party audits offered other advantages such as increased transparency and improvements in worker education and training. Finally, we present research propositions derived from our empirical study to guide future research on implementing social sustainability in emerging markets.