  We investigate how the galaxy reservoirs of molecular gas fuelling star
formation are transformed while the host galaxies infall onto galaxy cluster
cores. As part of the Spatially Extended ESO Distant Cluster Survey (SEEDisCS),
we present CO(3-2) observations of 27 star-forming galaxies obtained with the
Atacama Large Millimeter Array (ALMA). These sources are located inside and
around CL1411.1$-$1148 at $z=0.5195$, within five times the cluster virial
radius. These targets were selected to have stellar masses M$_{\rm star}$),
colours, and magnitudes similar to those of a field comparison sample at
similar redshift drawn from the Plateau de Bure high-$z$ Blue Sequence Survey
(PHIBSS2). We compare the cold gas fraction ($\mu_{\rm H_2}=$ M$_{\rm
H_2}$/M$_{\rm star}$), specific star formation rates (SFR/M$_{\rm star}$) and
depletion timescales ($t_{\rm depl}=$ M$_{\rm H_2}$/SFR) of our main-sequence
galaxies to the PHIBSS2 subsample. While the most of our galaxies (63\%) are
consistent with PHIBSS2, the remainder fall below the relation between
$\mu_\mathrm{H_2}$ and M$_{\rm star}$ of the PHIBSS2 galaxies at $z\sim0.5$.
These low-$\mu_\mathrm{H_2}$ galaxies are not compatible with the tail of a
Gaussian distribution, hence they correspond to a new population of galaxies
with normal SFRs but low gas content and low depletion times ($\lesssim 1$
Gyr), absent from previous surveys. We suggest that the star formation activity
of these galaxies has not yet been diminished by their low fraction of cold
molecular gas.
