  We consider a novel McKean--Vlasov control problem with contagion through
killing of particles and common noise. Each particle is killed at an
exponential rate according to an intensity process that increases whenever the
particle is located in a specific region. The removal of a particle pushes
others towards the removal region, which can trigger cascades that see
particles exiting the system in rapid succession. We study the control of such
a system by a central agent who intends to preserve particles at minimal cost.
Our theoretical contribution is twofold. Firstly, we rigorously justify the
McKean--Vlasov control problem as the limit of a corresponding controlled
finite particle system. Our proof is based on a controlled martingale problem
and tightness arguments. Secondly, we connect our framework with models in
which particles are killed once they hit the boundary of the removal region. We
show that these models appear in the limit as the exponential rate tends to
infinity. As a corollary, we obtain new existence results for McKean--Vlasov
SDEs with singular interaction through hitting times which extend those in the
established literature. We conclude the paper with numerical investigations of
our model applied to government control of systemic risk in financial systems.
