It refers to the nucleus of the family, which is where the jeans are stored (closet). Every conservative, Christian, god-fearing nuclear family has at least one family member in the closet. Usually, it’s Lindsey Graham. It’s always Lindsey Graham.

(I’m not implying that all homophobes are secretly gay. I know that’s a harmful view.)

As a ghoul I can confirm this is exactly what it meant.

Honestly I assumed it was the people you'd share your bomb shelter with for a while.

I thought it was that because they were exposed to radiation they couldn't have more than 2 kids and they had to live in neighborhoods with houses with extra radiation shielding!

Couldn't they have come up with a better name (core or base or immediate) ... ? Or was it on purpose?

Your username is unruly.