  The existence of giant planets on wide orbits ($\stackrel{>}{_\sim}100$AU)
challenge planet formation theories; the core accretion scenario has difficulty
in forming them, whereas the disc instability model forms an overabundance of
them that is not seen observations. We perform $N$-body simulations
investigating the effect of close stellar encounters ($\leq 1200$AU) on systems
hosting wide-orbit giant planets and the extent at which such interactions may
disrupt the initial wide-orbit planet population. We find that the effect of an
interaction on the orbit of a planet is stronger for high-mass, low-velocity
perturbers, as expected. We find that due to just a single encounter there is a
$\sim 17%$ chance that the wide-orbit giant planet is liberated in the field, a
$\sim 10$% chance it is scattered significantly outwards, and a $\sim 6$%
chance it is significantly scattered inwards. Moreover, there is a $\sim 21\%$
chance that its eccentricity is excited to e>0.1, making it more prone to
disruption in subsequent encounters. The results strongly suggest that the
effect of even a single stellar encounter is significant in disrupting the
primordial wide-orbit giant planet population; in reality the effect will be
even more prominent, as in a young star-forming region more such interactions
are expected to occur. We conclude that the low occurrence rate of wide-orbit
planets revealed by observational surveys does not exclude the possibility that
such planetary systems are initially abundant, and therefore the
disc-instability model may be a plausible scenario for their formation.
