  We consider a Fleming-Viot-type particle system consisting of independently
moving particles that are killed on the boundary of a domain. At the time of
death of a particle, another particle branches. If there are only two particles
and the underlying motion is a Bessel process on $(0,\infty)$, both particles
converge to 0 at a finite time if and only if the dimension of the Bessel
process is less than 0. If the underlying diffusion is Brownian motion with a
drift stronger than (but arbitrarily close to, in a suitable sense) the drift
of a Bessel process, all particles converge to 0 at a finite time, for any
number of particles.
