  A scalar field rolling down a potential with a large initial velocity results
in inflation of a finite duration. Such a scenario suppresses the scalar power
on large scales improving the fit to the cosmological data. We find that the
scenario leads to a hitherto unexplored situation wherein the boundary terms
dominate the contributions to the scalar bispectrum over the bulk terms. We
show that the consistency relation governing the non-Gaussianity parameter
$f_{_{\rm NL}}$ is violated on large scales and that the contributions at the
initial time can substantially enhance the value of $f_{_{\rm NL}}$.
