An agent is solvent but illiquid when its debt is not unsustainable but it has large amounts of this debt coming to maturity (i.e. short term debt) and it is not able to roll it over (this creates liquidity crisis, rollover/run crisis). Illiquidity can lead to insolvency as illiquidity can trigger default. In a liquidity crisis, international institutions may step in to provide emergency funds as a “lender of last resort”.