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

Extinction of Fleming-Viot-type particle systems with strong drift