NK can have a handful of submarine-based missiles that threaten to wipe out say Seoul or LA for example, even after the first strike. It's not a guarantee by any means but it does raise the bar and would probably prevent a situation like the current one.
NK kept itself safe for decades with just a lot of artillery aimed at Seoul.
Second strike weapons are in some ways a holdover from Cold War strategic thinking which it's sort of acknowledged probably overestimated the penchant of any side to engage in a first strike.
The practical reality of nuclear war planning has generally been that no one will accept even a single city-buster landing - and no first strike option is really reliable enough to guarantee you didn't miss one.
