I thought K-19 had a loss of coolant casualty (I.E. reactor coolant leak) not a loss of flow (I.E. loss of coolant pumps).
So long as there is liquid water present in the core, no major fuel element failure is expected. Thus the mantra “keep the core covered”. In practice this means it’s possible to pump the contents of pretty much any tank or system into the reactor coolant system by one means or another. Granted you’d be having an incredibly bad day if you were hooking up firehoses to the sanitary systems (which, incidentally, is the step you get to after you run out of seawater… that’s right, they have a scenario for when you’ve pumped the entire ocean into the reactor compartment :dubious:), but at least you’re not sitting in ankle deep glow-in-the-dark water two feet away from a steam leak in a rubber suit trying to finish before the lenses of your eyes turn opaque and the cataracts make you too blind to see what you’re welding.