This paper proposes an important extension to Conditional Value-at-Risk (CoVaR), the popular systemic risk measure, and investigates its properties on the cryptocurrency market. The proposed Vulnerability-CoVaR (VCoVaR) is defined as the Value-at-Risk (VaR) of a financial system or institution, given that at least one other institution is equal or below its VaR. The VCoVaR relaxes normality assumptions and is estimated via copula. While important theoretical findings of the measure are detailed, the empirical study analyses how different distressing events of the cryptocurrencies impact the risk level of each other. The results show that Litecoin displays the largest impact on Bitcoin and that each cryptocurrency is significantly affected if an event of joint distress among the remaining market participants occurs. The VCoVaR is shown to capture domino effects better than other CoVaR extensions.