The 1h (one-hole) and 2h-1p (two-hole; one-particle) shake-up bands in the valence ionization spectrum of small carbon chains (C-3,C-5,C-7,C-9) are investigated up to 40 eV, using the one-particle Green's function approach. Calculations have been performed at the second- and third-orders of an algebraic diagrammatic construction (ADC) scheme based on partial renormalization series, which incorporate static and dynamic electronic correlation consistently through those orders. The results obtained indicate a major or complete breakdown of the orbital picture of ionization extending down into the outer-valence energies for the largest chains (12.4 eV for C-9). Cumulenic carbon chains represent the only case reported so far where outer-valence ionization lines of pi character can be affected by severe fragmentation in shake-up sets. The one-hole states associated with the terminal carbon lone pairs are also very strongly affected by electronic relaxation.