Blazars, together with other active galactic nuclei, are the most luminous persistent sources in our universe; and therefore a prime candidate for very-high-energy (>0.2 TeV, VHE) gamma-ray observations. For the two MAGIC telescopes, the Mrk501 galaxy is among the brightest observed blazars due to its proximity. We report a multi-wavelength and multi-messenger study of Mrk501 with data from 2017 to 2020, when Mrk501 showed a VHE flux typically below 10% that of the Crab Nebula. During this time, we performed three long observations with NuSTAR, which characterized the hard X-ray emission during three different low-activity flux levels. This Mrk501 dataset provided the unprecedented opportunity to study multi-wavelength variability and correlations with sensitive instruments during historically low X-ray and VHE gamma-ray emission (below 5% of the Crab Nebula flux in the VHE range), which could be considered as the baseline emission of Mrk501. We complemented the broadband spectral energy distributions (SED) of the identified historically low X-ray and VHE gamma-ray flux with data published by IceCube, in order to evaluate the potential existence of a hadronic component that is stable (or slowly variable), and less visible than the leptonic component that may dominate the emission during typical and flaring activity. In this contribution, we will also describe the evolution of the broadband SED comparing different theoretical scenarios.
