Without a historical reference, I have doubts about the Black Death reference. Scholarship around the Black Death has changed.
The premise behind this question is that the velocity of money is constant. Since we can see that it is not - link to FRED M2 velocity - we need to ask what else drives the price level.
The obvious concern is that there is no explanation of how output falls 90%. Is it because of out-of-control bankruptcies causing business failures, while the government does nothing? That’s a deflationary environment. Was there a war or pandemic that destroyed industrial capacity? Probably inflationary.
If we step away from the text of the question, and just look at the title - does fractional reserve banking limit the shrinkage of the money supply - the answer is technically no. For the few remaining countries with reserve requirements, if deposits fall, so do required reserves. If the central bank keeps excess reserves at zero, then reserves will shrink along with deposits. As for currency in circulation, it is determined by the desire of the private sector to hold it. If holdings depend on incomes, holdings will fall in line with incomes.
What might keep the monetary base from shrinking is a deliberate policy choice of the central bank.