  [abridged] Building upon a previous study, we define a method to blindly
identify galaxies that underwent, and may still be undergoing, a fast downfall
of their star-formation activity, that is, a more than 80% drop in
star-formation rate (SFR) occurring in less than 500 Myr. Modeling galaxies'
SED with a delayed-$\tau$ star formation history (SFH), with and without
allowing an instantaneous SFR drop within the last hundreds Myr, we isolate 102
candidates out of a subsample of 6,680 galaxies classified as star-forming from
the UVJ criterion in the ZFOURGE catalogues. These galaxies are mostly located
in the lower part of the SFR-M$_*$ main sequence (MS) and extend up to a factor
100 below it. They also lie close to the limit between the passive and active
regions on the UVJ diagram, indicating that they are in a transition phase. We
show that the selected candidates have different physical properties compared
to galaxies with similar UVJ colors, namely, lower star-formation rates and
different stellar masses. The morphology of the candidates show no preference
for a particular type. Among the 102 candidates, only 4 show signs of an AGN
activity (from X-ray luminosity or UV-IR SED fitting decomposition). This low
fraction of AGNs among the candidates implies that AGN activity may not be the
main driver of the recent downfall, although timescale differences and duty
cycle must be taken into account. We finally attempt to recover the past
position of these galaxies on the SFR-M$_*$ plane, before the downfall of their
star-formation and show that some of them were in the starburst region before
and are back on the MS. These candidates constitute a promising sample that
need more investigation in order to understand the different mechanisms at the
origin of the star formation decrease of the Universe since $z$$\sim$2.
