In this paper we study the structural robustness of Italian business system, using Covid-19 pandemic as an exogenous event to test it. To this aim, we use the ROC (Receiver Operating Characteristics) methodology, quite new for Economics, to classify Italian firms according to their economic solidity, obtaining a taxonomy based on a wide set of characteristics. Our results show that the number of “Solid” firms are less than one fifth of the universe of Italian enterprises but they represent the lion share in terms of employment and value added. “Fragile” and “Risky” firms, albeit much less relevant for the creation of value added, account for over one third of total employment, so that they are a worrisome issue for policy makers. The pandemic crisis has clearly both a size and sector-related dimension: Risky and Fragile conditions prevail among firms with smaller economic size (a broad definition of firm size) and among those operating in Construction and Other services. Finally, we find that factors such as firms’ performance, internal and external organization, although significant, play a less relevant role than economic size and digitalization/innovation in determining Italian firms’ solidity to shocks such as the Covid-19 one.