In "Indiscretion" Kira is trapped in a cave with Dukat. They are thrust together for reasons. Anyway, at one point Dukat sits on a sharp rock and gets a major new hole, right near his old hole.

Kira gives Dukat a tool from the Starfleet issue medkit to heal the wound. Essentially he closes the new hole, but hopefully not the old hole. Both Kira and Dukat find this hilarious and they bond.

So a (butt)hole closer is the tool used to repair wounds.

What you should take away from this is: When Ben and Adam say (butt)hole closer they mean dermal regenerator.

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