'cross-fibered' is a modern compound formed from 'cross' + 'fiber' + the adjectival/past-participial suffix '-ed'; 'cross' denotes 'across' or 'intersecting', and 'fiber' denotes a thread or filament.

'fiber' originates from Latin 'fibra' (through Old French 'fibre'), meaning 'a filament or fiber'; 'cross' comes via Old English 'cros' (ultimately from Latin 'crux' meaning 'stake' or 'cross') but developed the sense 'across' in Germanic languages. The combination into a descriptive compound like 'cross-fibered' is a modern English formation describing the arrangement of fibers.

Initially, the elements meant 'a cross' and 'a filament', but combined in modern usage they specifically denote an arrangement in which filaments or fibers cross; the meaning evolved from the separate basic senses to a technical descriptive term.