The reserve ratio (which in most places is now down to 2% or less), is there to prevent runaway monetary expansion through lending/deposit creation. The Central Bank's role as lender of last resort is the backup for bank runs.
In the event of a run, a bank is considered illiquid, an insolvent bank is one where losses on debts exceed loss provisions and capital.
An entity that only wrote loans, and didn't have deposits would not be a bank - the definition of a bank is implicitly that it is performing fractional reserve banking via double entry book keeping. (Unless it's the World Bank, which is actually a fund, because the US and UK had an argument about who would control the International Monetary Fund (which is actually a bank) when the Bretton Woods agreement was setup.
No banks, including central banks can really be described as robust. They have at best around 1% fault tolerance in terms of the quantity of loans as a percentage of total lending that they can write-off each year.
Yes, that is about to become a huge problem.