If you loosen the truss rod too much releasing it from the captive nut close to fret 20 the whole rod can come all the way out.
Gibson truss rod nut.
Interestingly these nuts sit lower than the headstock facing so it looks like the damage occurred as the face of the headstock was being prepped to receive the overlaid facing.
You can use a 5 16 socket but i would recommend one of those gibson truss rod wrenches that looks like a little corn cob pipe but is usually black in color sometimes chrome.
16 futheda guitar truss rod wrench luthier screwdriver for taylor guitars silver 4 3 out of 5 stars 42.
They should have them wherever they sell gibson or aftermarket guitar parts.
The short taper leaves more metal for the hex sides which gives wrenches a good grip.
Guitar truss rod wrench luthier tool for 8mm 5 16 gibson nut brand new 3 9 out of 5 stars 3 9 16 9.
5 16 hex brass 5 16 length 10 32 thread.
Edited september 11 2019 by mihcmac.
Sometimes the truss rod can be really stuck requiring you to use a small adjustable wrench to turn the hex wrench.
It is usually not too hard to thread it back in.
Gibson started using the long taper nuts in the 1950s and continues to use them today.
Gibson used short taper truss rod nuts from the late teens into the early 1950s.
Truss rods and truss rod nuts allparts uk.
The truss rod adjustment on a gibson les paul is done using its brass nut at the headstock end of the neck located under the truss rod cover funnily enough.