Context. The continuous high-precision photometric observations provided by the CoRoT and Kepler space missions have allowed us to understand the structure and dynamics of red giants better using asteroseismic techniques. A small fraction of these stars show dipole modes with unexpectedly low amplitudes. The reduction in amplitude is more pronounced for stars with a higher frequency of maximum power, νmax. Aims: In this work we want to characterise KIC 8561221 in order to confirm that it is currently the least evolved star among this peculiar subset and to discuss several hypotheses that could help explain the reduction of the dipole mode amplitudes. Methods: We used Kepler short- and long-cadence data combined with spectroscopic observations to infer the stellar structure and dynamics of KIC 8561221. We then discussed different scenarios that could contribute to reducing the dipole amplitudes, such as a fast-rotating interior or the effect of a magnetic field on the properties of the modes. We also performed a detailed study of the inertia and damping of the modes. Results: We have been able to characterise 36 oscillations modes, in particular, a few dipole modes above νmax that exhibit nearly normal amplitudes. The frequencies of all the measured modes were used to determine the overall properties and the internal structure of the star. We have inferred a surface rotation period of ~91 days and uncovered a variation in the surface magnetic activity during the last 4 years. The analysis of the convective background did not reveal any difference compared to "normal" red giants. As expected, the internal regions of the star probed by the ℓ = 2 and 3 modes spin 4 to 8 times faster than the surface. Conclusions: With our grid of standard models we are able to properly fit the observed frequencies. Our model calculation of mode inertia and damping give no explanation for the depressed dipole modes. A fast-rotating core is also ruled out as a possible explanation. Finally, we do not have any observational evidence of a strong deep magnetic field inside the star. Table 3 and Appendix A are available in electronic form at http://www.aanda.org