  We aim to narrow down the origin of the non-detection of the metastable HeI
triplet at about 10830 A obtained for the hot Jupiter WASP-80b. 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 to infer the
extreme-ultraviolet (EUV) flux in the 200-504 A range, which controls the
formation of metastable HeI. We run three dimensional (magneto) hydrodynamic
simulations of the expanding planetary upper atmosphere interacting with the
stellar wind to study the impact on the HeI 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. For a low stellar
EUV emission, which is favoured by the measured logR'HK value, the HeI
non-detection can be explained by a solar He/H abundance ratio in combination
with a strong stellar wind, or by a sub-solar He/H abundance ratio, or by a
combination of the two. For a high stellar EUV emission, the non-detection
implies a sub-solar He/H abundance ratio. A planetary magnetic field is
unlikely to be the cause of the non-detection. The low EUV stellar flux, driven
by the low [Fe/O] coronal abundance, is the likely primary cause of the HeI
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
one to employ the 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 HeI atmospheric characterisation observations.
