Context . Linear C ₄ H and cyclic c -C ₃ H ₂ , as small unsaturated hydrocarbons, are the key precursors to complex organic molecules and are critical components of the interstellar medium. However, observational constraints on the evolution of these molecules in late-stage massive star-forming regions remain scarce. Aims . We present on-the-fly mapping observations of C ₄ H 9–8 lines, c -C ₃ H ₂ 2–1, H ¹³ CO ⁺ 1–0, and H42 α toward a sample of 22 massive star-forming regions using the IRAM 30 m telescope. Our aim is to further explore the evolution of these carbon-chain molecules by combining observational results obtained in cold cores. Methods . We employed H ¹³ CO ⁺ 1–0 and H42 α as tracers to probe the positions of molecular cloud cores and ionised hydrogen regions (H II regions), respectively. One chemical model in particular, which includes gas, dust grain surface, and icy mantle phases for C ₄ H and c -C ₃ H ₂ molecules, was used to make comparisons with observed abundances. Results . From mapping observations targeting 31 regions across 22 sources, C ₄ H 9–8 ( J = 19/2–17/2) and C ₄ H 9–8 ( J = 17/2–15/2) were detected in only 17 regions, while H ¹³ CO ⁺ 1–0 and c -C ₃ H ₂ 2–1 were successfully detected in all 31 regions. We find that the emission of C ₄ H 9–8 and c -C ₃ H ₂ 2–1 is concentrated at the edges of H42 α emission regions. The C ₄ H/H ¹³ CO ⁺ and c -C ₃ H ₂ /H ¹³ CO ⁺ relative abundance ratios range from 0.17 to 1.77 (median ~0.57) and 1.42 to 6.69 (median ~4.19), respectively, with a median C ₄ H/ c -C ₃ H ₂ ratio of 0.13. By combining the observational results of cold cores, we find that C ₄ H/H ¹³ CO ⁺ and c -C ₃ H ₂ /H ¹³ CO ⁺ ratios show a strong decreasing trend as molecular cores evolve. Conclusions . The decreasing trends in C ₄ H/H ¹³ CO ⁺ and c -C ₃ H ₂ /H ¹³ CO ⁺ ratios imply that small unsaturated hydrocarbons can be consumed and converted into other organic molecules during the evolution of molecular cores. The spatial concentration of C ₄ H and c -C ₃ H ₂ emission at the edges of H42 α regions further supports their role as precursors in the chemical pathways that lead to complex organic molecules in the interstellar medium.

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