The 2008 financial crisis has drawn attention to the concept of "too big to fail" companies, more recently relabelled "system-critical" institutions, referring to situations where the actual or near-bankruptcy of a company threatens the future of a service essential to the functioning of society. But such instances are not limited to the financial sector. We argue that if policymakers and regulators are not vigilant, a similar situation could occur in the electricity sector. So far this industry has only experienced occasional problems, but we can observe several precursory signals indicating that these problems might become more frequent. These include a tendency to globalisation in the absence of a supra-national regulator and the disruption caused by large amounts of renewable energies, resulting in companies being stranded with loss-making thermal generators. Still, these units are essential for the electricity supply security. We discuss several cases illustrating these trends. We conclude with a discussion of how electricity regulators and policymakers should approach the "too big to fail" problem, focussing both on preventive measures that can be taken to keep such a situation from occurring and on proactive actions aimed at avoiding a crisis once a system-critical company seems at risk of collapsing.