  In this work, we consider one-dimensional particles interacting in mean-field
type through a bounded kernel. In addition, when particles hit some barrier
(say zero), they are removed from the system. This absorption of particles is
instantaneously felt by the others, as, contrary to the usual mean-field
setting, particles interact only with other non-absorbed particles. This makes
the interaction singular as it happens through hitting times of the given
barrier. In addition, the diffusion coefficient of each particle is non
uniformly elliptic. We show that the particle system admits a weak solution.
Through Partial Girsanov transforms we are able to relate our particles with
independent stopped Brownian motions, and prove tightness and convergence to a
mean-fied limit stochastic differential equation when the number of particles
tends to infinity. Further, we study the limit and establish the existence and
uniqueness of the classical solution to the corresponding nonlinear
Fokker-Planck equation under some continuity assumption on the interacting
kernel. This yields the strong well-posedness of the mean-field limit SDE and
confirms that our convergence result is indeed a propagation of chaos result.
