Aims. We aim to constrain the origin of the non-detection of the metastable He I triplet at ≈10 830 Å obtained for the hot Jupiter WASP-80b. Methods. We measure the X-ray flux of WASP-80 from archival observations and use it as input to scaling relations accounting for the coronal [Fe/O] abundance ratio in order to infer the extreme-ultraviolet (EUV) flux in the 200–504 Å range, which controls the formation of metastable He I. We run three-dimensional (magneto) hydrodynamic simulations of the expanding planetary upper atmosphere interacting with the stellar wind to study the impact on the He I absorption of the stellar high-energy emission, the He/H abundance ratio, the stellar wind, and the possible presence of a planetary magnetic field up to 1 G. Results. For low-stellar-EUV emission, which is favoured by the measured log R′_HK value, the He I non-detection can be explained by a solar He/H abundance ratio in combination with a strong stellar wind, by a subsolar He/H abundance ratio, or by a combination of the two. For a high stellar EUV emission, the non-detection implies a subsolar He/H abundance ratio. A planetary magnetic field is unlikely to be the cause of the non-detection. Conclusions. The low-EUV stellar flux driven by the low [Fe/O] coronal abundance is the likely primary cause of the He I non-detection. High-quality EUV spectra of nearby stars are urgently needed to improve the accuracy of high-energy emission estimates, which would then enable the employment of observations to constrain the planetary He/H abundance ratio and the stellar wind strength. This would greatly enhance the information that can be extracted from He I atmospheric characterisation observations.