  In this work we consider a one-dimensional Brownian motion with constant
drift moving among a Poissonian cloud of obstacles. Our main result proves
convergence of the law of processes conditional on survival up to time $t$ as
$t$ converges to infinity in the critical case where the drift coincides with
the intensity of the Poisson process. The complements a previous result of T.
Povel, who considered the same question in the case where the drift is strictly
smaller than the intensity.
