I am working on modelling the risk that a bank's cash in one currency could not be converted into another currencies. This convertability risk has liquidity implacations for the asset liabilities management of the bank.
A "convertibility event" is not "FX markets closing down" but a cross-border risk event when a government decrees that its currency cannot be legally converted to another currency.
As 8 recall, Malaysia and Thailand did it in 1998; and South Korea and Ukraine seriously discussed it in later years, but never actually did.
A non-delivery contract (an NDF or embedded in another product) has no convertibility risk. Most other products involving physical currency do.
Do not confuse convertibility with transfer ability risk - another cross-border risk, when a government stops you from repatriating assets under its jurisdiction, irrespective of currency.