PKS 1510-089 is a flat spectrum radio quasar strongly variable in the optical and GeV range. To date, very high-energy (VHE, > 100 GeV) emission has been observed from this source either during long high states of optical and GeV activity or during short flares. Aims. We search for low-state VHE gamma-ray emission from PKS 1510-089. We characterize and model the source in a broadband context, which would provide a baseline over which high states and flares could be better understood. Methods. PKS 1510-089 has been monitored by the MAGIC telescopes since 2012. We use daily binned Fermi-LAT flux measurements of PKS 1510-089 to characterize the GeV emission and select the observation periods of MAGIC during low state of activity. For the selected times we compute the average radio, IR, optical, UV, X-ray, and gamma-ray emission to construct a low-state spectral energy distribution of the source. The broadband emission is modeled within an external Compton scenario with a stationary emission region through which plasma and magnetic fields are flowing. We also perform the emission-model-independent calculations of the maximum absorption in the broad line region (BLR) using two different models. Results. The MAGIC telescopes collected 75 hr of data during times when the Fermi-LAT flux measured above 1 GeV was below 3? × 10 -8 ? cm -2 ? s -1 , which is the threshold adopted for the definition of a low gamma-ray activity state. The data show a strongly significant (9.5¿) VHE gamma-ray emission at the level of (4.27 ± 0.61 stat ) × 10 -12 ? cm -2 ? s -1 above 150 GeV, a factor of 80 lower than the highest flare observed so far from this object. Despite the lower flux, the spectral shape is consistent with earlier detections in the VHE band. The broadband emission is compatible with the external Compton scenario assuming a large emission region located beyond the BLR. For the first time the gamma-ray data allow us to place a limit on the location of the emission region during a low gamma-ray state of a FSRQ. For the used model of the BLR, the 95% confidence level on the location of the emission region allows us to place it at a distance > 74% of the outer radius of the BLR. © ESO 2018.