  PKS 1510-089 is a flat spectrum radio quasar strongly variable in the optical
and GeV range. We search for low-state VHE gamma-ray emission from PKS
1510-089. We aim to characterize and model the source in a broad-band context,
which would provide a baseline over which high states and flares could be
better understood. 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
modelled within an External Compton scenario with a stationary emission region
through which plasma and magnetic field are flowing. We perform also 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 hrs of data during times when the Fermi-LAT flux measured above 1
GeV was below 3x10-8cm-2s-1, which is the threshold adopted for the definition
of a low gamma-ray activity state. The data show a strongly significant
(9.5{\sigma}) VHE gamma-ray emission at the level of
(4.27+-0.61stat)x10-12cm-2s-1 above 150GeV, a factor 80 smaller 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
broad-band emission is compatible with the EC 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% C.L. on the
location of the emission region allows us to place it at the distance >74% of
the outer radius of the BLR.
