The ship can operate for a bit on decay heat. And they have battery banks to run major systems until conditions allow running at snorkel depth on the diesel engine.

And rumor has it some of the nuclear subs may work with a Stirling engine which can operate systems on heat alone.

I'd imagine the operational capabilities of nuclear submarines are somewhat confidential.

Warships have a “battle short” on some critical equipment, which will bypass safety equipment like fuses. If your gun turret traversal motors pull too much current in the middle of a battle, you’d rather risk damage or fire to have them keep working rather than disable themselves to protect from a fault. Total speculation here, but it would make sense for military reactors to have something similar, to put them in a mode where the threat of a reactor accident due to a malfunction is less than the threat from the enemy if it goes down. https://en.wikipedia.org/wiki/Battleshort

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