This answer is specifically about guitars because I have guitar building and repair experience.
The strings and the truss rod are under tension so the neck itself is mainly under compression. There is some tension on the back side of the neck due to neck relief (forward bow of neck) but not much. Necks are made from wood from the trunk, a material 'built' to handle the compressive stress from the weight of the tree.
The safety factor (failure load/service load)of guitar necks are very large.
A very basic calc. to demonstrate this:
Compressive yield strength parallel to grain for the most common guitar neck wood (maple) = 21.5 M Pa
Approximate Cross sectional area = 0.0007 m ^2
F = PA = (21.5 M Pa) * (0.0007 m^2) = 15 Kilo Newtons.
SF = (failure load/service load) = (15 kN)/(800 N) = 18.75
Basically, guitar necks are super strong and only fail due to impact (see Gibsons broken headstock syndrome) or warp due to poorly seasoned wood or extreme humidity or temp. changes.