The purpose of a legal requirement to report a lost or missing gun, is to allow for prosecution of a person who does not have a firearm listed in a gun registration scheme.
If a person is ordered to turn in a registered gun, and they say: I don't know what happened to it, they can be prosecuted for not reporting it.
Here is an essay explaining the gambit.
Well, I'd be screwed. We don't
have gun registration; I didn't think it was allowed under
federal law.
Your Constitution-defying state may differ. Hawaii?